
835 So.2d 990 (2002)
SouthTRUST BANK
v.
Melody FORD and Eddie Ford.
1010124.
Supreme Court of Alabama.
May 17, 2002.
*991 A. Joe Peddy and Clair Maloney Gammill of Smith, Spires & Peddy, P.C., Birmingham, for appellant.
Chuck Hunter, Birmingham, for appellees.
STUART, Justice.
SouthTrust Bank ("SouthTrust") is a defendant in an action pending in the Jefferson Circuit Court. It appeals from the trial court's denial of its motion to compel arbitration. We affirm in part, reverse in part, and remand with instructions.

Facts
Melody Ford and Eddie Ford are husband and wife. Upon the death of Melody's father, Edwin Edwards, Melody was appointed the administratrix of his estate. At the time of Edwards's death, he maintained at least one checking account with SouthTrust. Before his death, Edwards and SouthTrust were involved in a dispute regarding SouthTrust's payment of an allegedly *992 forged check drawn on Edwards's account.[1]
Edwards's checking account with South-Trust was governed by a "deposit agreement." That deposit agreement incorporated by reference SouthTrust's "Rules and Regulations Governing Deposit Accounts" and all amendments thereto. Those rules and regulations contained the following arbitration provision:
"ARBITRATION OF DISPUTES. You and we agree that the transactions in your account, involve `commerce' under the Federal Arbitration Act (`FAA'). ANY CONTROVERSY OR CLAIM BETWEEN YOU AND US, OR BETWEEN YOU AND ANY OF OUR OFFICERS, EMPLOYEES, AGENTS OR AFFILIATED ENTITIES, THAT ARISES OUT OF OR IS RELATED TO YOUR ACCOUNT, OR ANY AGREEMENT RELATED TO YOUR ACCOUNT, OR ANY SERVICE RELATED TO YOUR ACCOUNT OR ANY SUCH SERVICE, WHETHER BASED ON CONTRACT OR IN TORT OR ANY OTHER LEGAL THEORY, INCLUDING CLAIMS OF FRAUD, SUPPRESSION, MISREPRESENTATION AND FRAUD IN THE INDUCEMENT (COLLECTIVELY, ANY `CLAIM'), WILL BE SETTLED BY BINDING ARBITRATION UNDER THE FAA. EACH PARTY WAIVES ALL RIGHTS TO TRIAL IN ANY DISPUTE RELATED TO THESE RULES OR TO ANY RELATED SERVICE.... This agreement to arbitrate disputes will survive the closing of your account and the termination of your deposit agreement with us."
The Fords instituted this action against SouthTrust, alleging that SouthTrust: (1) negligently cashed a forged item drawn on Edwards's account; (2) intentionally inflicted emotional distress by causing Edwards's estate to be depleted and "having to vainly attempt to have [SouthTrust] reimburse the Monies and having to deal with Uncaring and Rude personnel of [SouthTrust]"; and (3) intentionally misrepresented and suppressed material facts concerning the passing and forgery of the check.
SouthTrust filed a motion to dismiss or, in the alternative, to stay the proceedings and compel arbitration. In support of that motion, SouthTrust submitted the affidavit of Heather Thornburgh, who is employed by SouthTrust as a vice president.
The Fords opposed SouthTrust's motion to compel arbitration. They asserted that the language of the deposit agreement and the language of the arbitration agreement itself pertained only to a dispute between Edwards and SouthTrust and that neither the deposit agreement nor the arbitration agreement addressed claims asserted by the administratrix of Edwards's estate.
The trial court denied SouthTrust's motion to compel arbitration, finding that the "substantial-effect-on-interstate-commerce" requirement had been satisfied but that the arbitration agreement did not apply to claims asserted by the depositor's agents, assigns, or representatives. SouthTrust appeals from the trial court's denial of its motion to compel arbitration.

Standard of Review
In American General Finance, Inc. v. Morton, 812 So.2d 282, 284 (Ala. *993 2001), Justice Harwood, writing the main opinion, set forth the standard of review on an appeal from the trial court's denial of a motion to compel arbitration:
"This Court reviews the denial of a motion to compel arbitration de novo. Green Tree Fin. Corp. v. Vintson, 753 So.2d 497, 502 (Ala.1999); Patrick Home Ctr., Inc. v. Karr, 730 So.2d 1171, 1172 (Ala.1999). The party seeking to compel arbitration has the initial burden of proving the existence of a contract calling for arbitration and proving that the contract evidences a transaction substantially affecting interstate commerce. TranSouth Fin. Corp. v. Bell, 739 So.2d 1110, 1114 (Ala.1999); Sisters of the Visitation v. Cochran, 775 So.2d 759 (Ala. 2000). `[A]fter a motion to compel arbitration has been made and supported, the burden is on the nonmovant to present evidence that the supposed arbitration agreement is not valid or does not apply to the dispute in question.' Jim Burke Auto., Inc. v. Beavers, 674 So.2d 1260, 1265 n. 1 (opinion on application for rehearing) (Ala.1995)."
Here, SouthTrust bears the initial burden of proving the existence of a contract calling for arbitration and proving that the contract evidences a transaction substantially affecting interstate commerce.
If SouthTrust met this burden of proof, then the burden of persuasion shifted to the Fords as the parties opposing the motion to compel arbitration. Once that burden has shifted, we consider whether the Fords have established that the arbitration agreement is inapplicable or whether they have a valid defense to the enforcement of that agreement.

Has SouthTrust Met its Burden of Proof?
The parties do not dispute that Edwards's checking account was governed by SouthTrust's deposit agreement, or that the deposit agreement included the arbitration agreement. Thus, SouthTrust established the existence of a contract calling for arbitration.
SouthTrust also presented evidence concerning the effect of its banking activities on interstate commerce; the trial court held that SouthTrust had proved that the transaction had a substantial effect on interstate commerce. On appeal, the Fords do not challenge SouthTrust's assertion or the trial court's finding that the transaction at issue in this case had a substantial effect on interstate commerce. Thus, the burden of persuasion shifted to the Fords to oppose SouthTrust's properly supported motion to compel arbitration.

The Fords' Defenses to the Arbitration Provision
The Fords oppose arbitration because, they allege, SouthTrust's deposit agreement governs only a transaction between SouthTrust and Edwards and does not include Edwards's estate. They further assert that the language of the arbitration agreement itself does not encompass the claims asserted by a depositor's agents, assigns, or representatives but limits the application of the agreement solely to disputes between Edwards and SouthTrust.
We recognize that an administratrix of a decedent's estate stands in the shoes of the decedent. See Conseco Fin. Corp. v. Sharman, 828 So.2d 890 (Ala. 2001). We also recognize that the "[p]owers [of an executor], in collecting the debts constituting the assets of the estate, are just as broad as those of the deceased." Webb v. Sprott, 144 So. 569, 571, 225 Ala. 600, 603 (1932). For the same reason the powers of an executor or an administrator encompass all of those formerly held by the decedent, those powers must likewise be restricted in the same manner and to the same extent as the powers of the decedent *994 would have been. Thus, where an executor or administrator asserts a claim on behalf of the estate, he or she must also abide by the terms of any valid agreement, including an arbitration agreement, entered into by the decedent.
We agree that the arbitration agreement at issue in this case is limited to disputes arising between Edwards and SouthTrust. If Edwards were alive and asserting against SouthTrust a claim to recover the value of the purportedly forged check, he would be bound to arbitrate. Because Melody serves as the administratrix of Edwards's estate, she stands in his shoes. We conclude that Melody's claim to recover the value of the improperly paid check is subject to arbitration because she is asserting that claim in her role as the administratrix of Edwards's estate.
Additionally, Edwards agreed to arbitrate any dispute with SouthTrust "that arises out of or is related to [his] account, or any agreement related to [his] account, ... whether based on contract or in tort." Thus, to the extent that Melody's tort claims of intentional infliction of emotional distress and fraud are based upon an injury sustained by Edwards before his death, those claims would be subject to the agreement to arbitrate. This Court, however, expresses no opinion as to whether any such claims survived Edwards's death. See § 6-5-462, Ala.Code 1975 ("In all proceedings not of an equitable nature, all claims upon which an action has been filed and all claims upon which no action has been filed on a contract, express or implied, and all personal claims upon which an action has been filed, except for injuries to the reputation, survive in favor of and against personal representatives; and all personal claims upon which no action has been filed survive against the personal representative of a deceased tortfeasor.").
However, this Court has noted: "`"[A]rbitration is a matter of contract and a party cannot be required to submit to arbitration any dispute which he has not agreed so to submit."'" Modern Woodmen of America v. McElroy, 815 So.2d 520, 526 (Ala.2001), quoting AT & T Techs., Inc. v. Communications Workers of America, 475 U.S. 643, 648, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986), quoting in turn United Steelworkers v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). Although this Court has recognized certain situations in which an agreement to arbitrate may extend to nonsignatories, see, e.g., Oakwood Mobile Homes, Inc. v. Godsey, 824 So.2d 713 (Ala.2001) (discussing third-party beneficiaries and the doctrine of intertwining), those limited exceptions are not applicable in this case.
First, Melody has not agreed to arbitrate her claims against SouthTrust. Additionally, if Melody is asserting a tort claim based upon an injury she suffered directly, she is not seeking the benefits of the Edwards-SouthTrust deposit agreement. Thus, she is not a third-party beneficiary of that contract. See, e.g., Tom Williams Motors, Inc. v. Thompson, 726 So.2d 607 (Ala.1998) (the father was not a third-party beneficiary of the contract containing an arbitration provision; he was not a signatory to the contract, his claims were independent of the contract, and he was not seeking to recover benefits due under that contract).
The only possible basis for compelling Melody to arbitrate any personal claims she might have against SouthTrust would be under the doctrine of "intertwining." The doctrine of intertwining is applicable where arbitrable and nonarbitrable claims are so closely related that the party to a controversy subject to arbitration is *995 equitably estopped from denying the arbitrability of the related claim. See, e.g., Ex parte Tony's Towing, Inc., 825 So.2d 96 (Ala.2002); Oakwood Mobile Homes, Inc. v. Godsey, supra; Cook's Pest Control, Inc. v. Boykin, 807 So.2d 524 (Ala.2001).
However, the doctrine of equitable estoppel is not applicable where the arbitration agreement is specifically limited to the parties that have executed the agreement. Monsanto Co. v. Benton Farm, 813 So.2d 867 (Ala.2001). The arbitration provision at issue in this case encompasses only disputes that arose between Edwards and SouthTrust.
Moreover, the doctrine of estoppel is applicable only to estop a signatory from avoiding arbitration. See Ex parte Tony's Towing, Inc., supra (noting that a nonsignatory cannot be estopped from avoiding arbitration and recognizing that the equitable principle of intertwining is applicable only where a signatory to the arbitration agreement seeks to frustrate a nonsignatory from obtaining arbitration). Because arbitration is strictly a matter of contract, this Court has no authority, even under the doctrine of equitable estoppel, to compel parties to arbitrate if they have not agreed to do so. Because Melody has never agreed to submit her personal claims against SouthTrust to arbitration, the doctrine of intertwining is not applicable to any claims asserted by her on her own behalf.
We are unable to determine from the record the factual allegations underlying Melody's claims of intentional infliction of emotional distress and fraud. Accordingly, the trial court is instructed to conduct further proceedings as necessary to determine which, if any, of Melody's tort claims are asserted on behalf of Edwards's estate and which, if any, are asserted on her own behalf. The trial court is instructed to then determine, consistent with this opinion, which of those claims are subject to arbitration.
We now address Eddie's claims.[2] Like Melody, Eddie is not a signatory to the arbitration agreement. He is not a third-party beneficiary under the Edwards-SouthTrust deposit agreement, and the arbitration agreement incorporated in that contract is specifically limited to disputes arising between Edwards and SouthTrust. For these reasons, the reasoning we applied to Melody's claims is equally applicable to the claims asserted by Eddie.
Nothing in the record suggests that Eddie is asserting his claims in any capacity other than an individual one. Because Eddie is not a signatory to the arbitration agreement and because he has not agreed to arbitrate his claims against SouthTrust, his claims are not subject to the arbitration agreement. Again, we express no opinion as to the viability of any of the claims asserted in the complaint.

Conclusion
SouthTrust has properly supported its motion to compel arbitration of the claims asserted on behalf of Edwards's estate. Any claim asserted by Melody on behalf of Edwards's estate is subject to the agreement to arbitrate. However, any claim asserted on behalf of Melody or Eddie personally is not subject to arbitration. We affirm the trial court's order of August 26, 2001, insofar as it pertains to any claim asserted by Melody or Eddie in their personal capacity; we reverse the trial court's order insofar as it pertains to any claims asserted by Melody in her role as the administratrix of Edwards's estate; and we remand this case to the trial court for *996 further proceedings consistent with this opinion.
AFFIRMED IN PART; REVERSED IN PART; REMANDED WITH INSTRUCTIONS.
HOUSTON, SEE, LYONS, BROWN, JOHNSTONE, HARWOOD, and WOODALL, JJ., concur.
MOORE, C.J., concurs in the result in part and dissents in part.
MOORE, Chief Justice (concurring in the result in part and dissenting in part).
I concur in affirming the trial court's order denying arbitration as to the claims asserted by Melody and Eddie Ford in their individual capacities; however, I dissent from the reversal of the trial court's denial of arbitration as to the claims asserted by Melody Ford in her role as administratrix.
NOTES
[1]  Eddie is not named as the administrator of Edwards's estate, and the record is devoid of any basis upon which Eddie could proceed to recover the value of the purportedly forged check on behalf of Edwards's estate. We also find nothing in the record to suggest that Eddie would have a personal cause of action to recover the value of the purportedly forged check.
[2]  See note 1.
