Iterates of a compact holomorphic map on a finite rank homogeneous ball
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 H...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-018-518-z |
| Online Access: | http://acta.bibl.u-szeged.hu/62142 |
| LEADER | 01697nab a2200241 i 4500 | ||
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| 001 | acta62142 | ||
| 005 | 20260219130812.0 | ||
| 008 | 190925s2019 hu o 000 eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-018-518-z |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Mackey M. | |
| 245 | 1 | 0 | |a Iterates of a compact holomorphic map on a finite rank homogeneous ball |h [elektronikus dokumentum] / |c Mackey M. |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2019 | ||
| 300 | |a 203-214 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 85 No. 1-2 | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Mellon P. |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/62142/1/math_085_numb_001-002_203-214.pdf |z Dokumentum-elérés |