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||Journal:||Journal of Mathematical Analysis and Applications||Volume:||456||Issue:||1||Start page:||57||End page:||68||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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