
894 A.2d 408 (2006)
In re Mary CALOMIRIS, George Calomiris, Appellant.
No. 05-PR-1454.
District of Columbia Court of Appeals.
March 2, 2006.
Before FARRELL and FISHER, Associate Judges, and KING, Senior Judge.
FISHER, Associate Judge:
Appellant George Calomiris is one of four trustees of the William Calomiris Marital Trust. The other trustees are his siblings. A dispute over administration of the trust led to litigation in the Superior Court, and the trustees filed cross-claims for removal. Appellant wants the court to remove his siblings as trustees; they want him removed. Appellant filed a motion for summary judgment arguing that the claims should be dismissed because a provision in the will directed that any material difference of opinion among the trustees be resolved by arbitration. The trial court denied appellant's motion for summary disposition, concluding that the trust did not give an arbitrator the power to remove trustees. Appellant promptly filed this pretrial appeal.
This court subsequently issued an order directing appellant to show cause why this appeal should not be dismissed for lack of jurisdiction as having been taken from a non-final order, and appellees filed a motion to dismiss asserting a similar jurisdictional defect. Appellant responded by arguing two alternative theories. His first argument is based upon D.C.Code § 16-4317, which provides that (in circumstances we will discuss later) an order denying a motion to compel arbitration is a final appealable order. See Hercules & Co. v. Beltway Carpet Serv., Inc., 592 A.2d 1069, 1072 (D.C.1991). The alternative argument submitted by appellant is that if *409 the order is not deemed final for purposes of appeal, it is nonetheless appealable on an interlocutory basis as the trial court has "frustrated" the arbitration process. See Brandon v. Hines, 439 A.2d 496, 507 (D.C. 1981). We reject appellant's arguments and dismiss the appeal.
Ordinarily the denial of a motion for summary judgment is not an appealable order. See Allen v. Yates, 870 A.2d 39, 45 (D.C.2005). However, appellant's motion specifically argued, among other things, that "cross-claimants must submit their request for Mr. Calomiris' removal as trustee to arbitration." In Hercules, we held that a motion to dismiss on the ground that the underlying contract required arbitration should be treated as a motion to compel arbitration. Therefore, we concluded, the denial of the motion to dismiss was immediately appealable under D.C.Code § 16-4317. 592 A.2d at 1072. We similarly construe the denial of appellant's motion for summary judgment as the denial of an application to compel arbitration. However, this conclusion does not resolve the question of our jurisdiction. In order to determine whether that order is immediately appealable under § 16-4317, we must look more closely at the statute.
The Uniform Arbitration Act, which has been adopted in the District of Columbia, instructs us to treat as final (and thus appealable) an "order denying an application to compel arbitration made under section 16-4302." D.C.Code § 16-4317(a)(1) (2001). An application under the referenced section must show "an agreement described in section 16-4301,"[1] which in turn requires, as relevant here, "[a] written agreement to submit any existing controversy to arbitration or a provision in a written contract to submit to arbitration any controversy thereafter arising between the parties."[2] As we recognized in Meshel v. Ohev Sholom Talmud Torah, 869 A.2d 343, 361 (D.C.2005), "D.C.Code §§ 16-4301 and 16-4302(a) require a court considering an action to compel arbitration to determine, according to traditional principles of contract law,[3] whether the parties have an enforceable agreement to arbitrate and, if so, whether the underlying dispute between the parties falls within the scope of the agreement." Although in addressing the question of our jurisdiction in this case we are not required to decide the scope of any arbitration agreement, we must determine whether the parties were required to engage in arbitration by "a provision in a written contract." If there is no written agreement or contract requiring arbitration, § 16-4317 would not apply. Ironically, therefore, we must touch upon the merits of this dispute in order to determine whether we have jurisdiction to hear this pretrial appeal.
As Judge Burgess explained, in the present case the arbitration clause is not contained in a written agreement or a contract. Rather, it is contained in the will establishing the trust. Like the trial court, we find instructive a decision from Arizona that addressed a similar issue. Construing its local counterpart to D.C.Code § 16-4301, the Arizona Court of Appeals held that "a trust is not a `written contract' requiring arbitration." Schoneberger v. Oelze, 208 Ariz. 591, 96 P.3d 1078, *410 1079 (App.2004). The Arizona court explained that "arbitration is a creature of contract law . . . [and] an inter vivos trust is not a contract." Id. at 1082.
Arbitration rests on an exchange of promises. Parties to a contract may decide to exchange promises to substitute an arbitral for a judicial forum. Their agreement to do so may end up binding (or benefitting) nonsignatories. In contrast, a trust does not rest on an exchange of promises. A trust merely requires a trustor to transfer a beneficial interest in property to a trustee who, under the trust instrument, relevant statutes and common law, holds that interest for the beneficiary. The undertaking between trustor and trustee does not stem from the premise of mutual assent to an exchange of promises and is not properly characterized as contractual.
Schoneberger, 96 P.3d at 1083 (internal quotation marks and citations omitted). Our case is slightly different because the arbitration provision is contained in a will, not the trust instrument. This distinction makes no difference, however, because a will is not a contract either. See, e.g., Bates's Estate, 286 Pa. 583, 134 A. 513 (1926); Martz's Ex'r v. Martz's Heirs, 66 Va. 361, 365 (1874).
In the absence of a contractual agreement to arbitrate, the trial court's order may not be appealed as a final order under § 16-4317. See DSMC Inc. v. Convera Corp., 358 U.S.App. D.C. 356, 360, 349 F.3d 679, 683 (2003) ("we hold that this court has no jurisdiction under Section 16(a)(1)(B) [of the Federal Arbitration Act, 9 U.S.C. § 16(a)(1)(B)] to hear an appeal of an order denying a motion to compel arbitration between parties not under a written agreement to arbitrate") (emphasis in original); Universal Serv. Fund Tel. Billing Practice Litig. v. Sprint Commc'ns Co., 428 F.3d 940, 942 (10th Cir.2005) ("the plain language of the applicable jurisdictional statute mandates Defendants' prior reliance upon a written agreement to arbitrate as a condition precedent to our jurisdiction" (emphasis in original); construing Federal Arbitration Act).[4] Nor do we understand Brandon v. Hines to confer a right to appeal under these circumstances. Although Brandon contains a comprehensive discussion of the appealability of interlocutory orders granting or denying stays of litigation pending arbitration, it held "that the trial court's order denying appellant's motion to confirm the arbitration award, vacating the award, and ordering the parties to trial, [was] an appealable interlocutory order dissolving an injunction." 439 A.2d at 509 (quotation marks omitted). See also id. at 500 (describing trial court order and holding of this court). Moreover, the contract at issue contained an arbitration clause, id. at 497, and the discussion of this court was predicated on the assumption "that the parties by contract had agreed to use" the arbitration process. Id. at 507. The extended discussion of the appealability of interlocutory orders was necessary because the District of Columbia Uniform Arbitration Act did not apply to the contract at issue. Id. at 501 n. 2. Nothing in Brandon suggests that the denial of a motion to compel arbitration is appealable in an interlocutory posture if the parties have not agreed to submit the dispute to arbitration. See Hercules & Co. v. Shama Rest. Corp., 566 A.2d 31, 39 (D.C.1989) (concluding that although recent Supreme Court and federal decisions "did not change District law as *411 announced in Brandon, they surely counsel us not to expand the scope of what may be appealed on a piecemeal basis beyond what Brandon requires").
Accordingly, this appeal is hereby dismissed for lack of jurisdiction.[5]
So ordered.
NOTES
[1]  D.C.Code § 16-4302(a).
[2]  D.C.Code § 16-4301.
[3]  In AT & T Technologies, Inc. v. Communications Workers of America, 475 U.S. 643, 648, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986), the Supreme Court explained that "[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" (citation omitted).
[4]  We previously have noted the similarity between D.C.Code § 16-4317 and the appealability provision of the Federal Arbitration Act, then codified at 9 U.S.C. § 15(a)(1)(B). See Hercules & Co., 592 A.2d at 1071 & n. 6.
[5]  In a separate proceeding (No. 06-OA-1) appellant seeks a writ of prohibition requiring the trial court to stay all proceedings until this appeal is resolved. In light of our disposition of this appeal, we are by separate order denying that petition as moot. We also deny appellees' motion for costs and attorneys' fees.
