Iterates of a compact holomorphic map on a finite rank homogeneous ball

Mackey, M. and Mellon, P.: Iterates of a compact holomorphic map on a finite rank homogeneous ball. Acta scientiarum mathematicarum, (85) 1-2. pp. 203-214. (2019)

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Abstract

We study iterates, f n , of a fixed-point free compact holomorphic map f : B → B where B is the open unit ball of any JB∗ -triple of finite rank. These spaces include L(H, K), H, K Hilbert, dim(H) arbitrary, dim(K) < ∞, or any classical Cartan factor or C -algebra of finite rank. Apart from the Hilbert ball, the sequence of iterates (f n )n does not generally converge (locally uniformly on B) and little is known of accumulation points. We present a short proof of a Wolff theorem for B and establish key properties of the resulting f-invariant subdomains. We define a concept of closed convex holomorphic hull, Ch(x), for x ∈ ∂B and prove the following. There is a unique tripotent u in ∂B such that all constant subsequential limits of (f n )n lie in Ch(u). As a consequence we also get a short proof of the classical Hilbert ball results.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
Page Range: pp. 203-214
ISSN: 2064-8316
DOI: https://doi.org/10.14232/actasm-018-518-z
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 212-214. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Sep. 25. 10:32
Last Modified: 2019. Sep. 25. 10:32
URI: http://acta.bibl.u-szeged.hu/id/eprint/62142

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