| Title:
|
On reflexivity and hyperreflexivity of some spaces of intertwining operators (English) |
| Author:
|
Zajac, Michal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
75-83 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T,T^{\prime }$ be weak contractions (in the sense of Sz.-Nagy and Foiaş), $m,m^{\prime }$ the minimal functions of their $C_0$ parts and let $d$ be the greatest common inner divisor of $m,m^{\prime }$. It is proved that the space $I(T,T^{\prime })$ of all operators intertwining $T,T^{\prime }$ is reflexive if and only if the model operator $S(d)$ is reflexive. Here $S(d)$ means the compression of the unilateral shift onto the space $H^2\ominus dH^2$. In particular, in finite-dimensional spaces the space $I(T,T^{\prime })$ is reflexive if and only if all roots of the greatest common divisor of minimal polynomials of $T,T^{\prime }$ are simple. The paper is concluded by an example showing that quasisimilarity does not preserve hyperreflexivity of $I(T,T^{\prime })$. (English) |
| Keyword:
|
intertwining operator |
| Keyword:
|
reflexivity |
| Keyword:
|
$C_0$ contraction |
| Keyword:
|
weak contraction |
| Keyword:
|
hyperreflexivity |
| MSC:
|
47A10 |
| MSC:
|
47A15 |
| MSC:
|
47A45 |
| idZBL:
|
Zbl 1199.47024 |
| idMR:
|
MR2400152 |
| DOI:
|
10.21136/MB.2008.133939 |
| . |
| Date available:
|
2009-09-24T22:34:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133939 |
| . |
| Reference:
|
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