Mellon, PaulinePaulineMellon2018-04-112017 Elsev2017-12-01Journal of Mathematical Analysis and Applicationshttp://hdl.handle.net/10197/9320We present a Wolff Theorem for all infinite dimensional bounded symmetric domains of finite rank. Namely, if Bis the open unit ball of any finite rank JB∗-triple and f:B→Bis a compact holomorphic map with no fixed point in B, we prove convex f-invariant subdomains of B(of all sizes and at all points) exist in the form of simple operator balls cλ+Tλ(B), for cλ∈Band Tλan invertible linear map. These are exact infinite dimensional analogues of the invariant discs in Δ, the invariant ellipsoids in the Hilbert ball and invariant domains in finite dimensional triples. Results are new for rank >2, even for classical spaces such as C∗-algebras and JB∗-algebras in finite dimensional analogues of the invariant discs in Δ, the invariant ellipsoids in the Hilbert ball and invariant domains in finite dimensional triples. Results are new for rank > 2, even for classical spaces such as C*-algebras and JB*-algebras.enThis is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications (456, 1, (2017)) DOI:10.1016/j.jmaa.2017.06.084Wolff TheoremBounded symmetric domainsFinite rankDenjoy-WolffJournal Article4561576810.1016/j.jmaa.2017.06.0842017-08-28https://creativecommons.org/licenses/by-nc-nd/3.0/ie/