On reflexivity and hyperreflexivity of some spaces of intertwining operators

Title:

On reflexivity and hyperreflexivity of some spaces of intertwining operators

Creator:

Zajac, Michal

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3dde6293-b202-4a2c-9f30-ca782eca75e6
uuid:3dde6293-b202-4a2c-9f30-ca782eca75e6
doi:10.21136/MB.2008.133939

Subject:

intertwining operator, reflexivity, C0 contraction, weak contraction, and hyperreflexivity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let T, T′ be weak contractions (in the sense of Sz.-Nagy and Foia¸s), m, m′ the minimal functions of their C0 parts and let d be the greatest common inner divisor of m, m′ . It is proved that the space I(T, T′ ) of all operators intertwining T, T′ 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 ⊖dH2 . In particular, in finite-dimensional spaces the space I(T, T′ ) is reflexive if and only if all roots of the greatest common divisor of minimal polynomials of T, T′ are simple. The paper is concluded by an example showing that quasisimilarity does not preserve hyperreflexivity of I(T, T′ ).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

75-83

Source:

Mathematica bohemica | 2008 Volume:133 | Number:1

Harvested from:

CDK

Metadata only:

false