A Wolff Theorem for finite rank bounded symmetric domains

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Title: A Wolff Theorem for finite rank bounded symmetric domains
Authors: Mellon, Pauline
Permanent link: http://hdl.handle.net/10197/9320
Date: 1-Dec-2017
Abstract: We 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.
Type of material: Journal Article
Publisher: Elsevier
Copyright (published version): 2017 Elsevier
Keywords: Wolff Theorem;Bounded symmetric domains;Finite rank;Denjoy-Wolff
DOI: 10.1016/j.jmaa.2017.06.084
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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