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...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2019
|
| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-018-518-z |
| Online Access: | http://acta.bibl.u-szeged.hu/62142 |
| Tartalmi kivonat: | 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. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 203-214 |
| ISSN: | 2064-8316 |