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Ergodic properties of operators in some semi-Hilbertian spaces

Suciu, Laurian LU ; Majdak, Witold and Secelean, Nicolae (2012) In Linear and Multilinear Algebra 61(2). p.139-159
Abstract
This article deals with linear operators T on a complex Hilbert space , which are bounded with respect to the seminorm induced by a positive operator A on . The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesàro ergodic, such that T  * is not a quasiaffine transform of an orthogonally mean ergodic... (More)
This article deals with linear operators T on a complex Hilbert space , which are bounded with respect to the seminorm induced by a positive operator A on . The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesàro ergodic, such that T  * is not a quasiaffine transform of an orthogonally mean ergodic operator. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Cesàro ergodic operator, orthogonally mean ergodic operator, A-power bounded operator, quasiaffine transform
in
Linear and Multilinear Algebra
volume
61
issue
2
pages
139 - 159
publisher
Taylor & Francis
external identifiers
  • wos:000311777300001
  • scopus:84870943158
ISSN
1026-7573
DOI
10.1080/03081087.2012.667094
language
English
LU publication?
yes
id
b1c8aa89-3711-48a2-b0a2-578fa0a8b65c (old id 2856887)
date added to LUP
2013-09-16 12:30:17
date last changed
2017-01-01 03:09:04
@article{b1c8aa89-3711-48a2-b0a2-578fa0a8b65c,
  abstract     = {This article deals with linear operators T on a complex Hilbert space , which are bounded with respect to the seminorm induced by a positive operator A on . The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesàro ergodic, such that T  * is not a quasiaffine transform of an orthogonally mean ergodic operator.},
  author       = {Suciu, Laurian and Majdak, Witold and Secelean, Nicolae},
  issn         = {1026-7573},
  keyword      = {Cesàro ergodic operator,orthogonally mean ergodic operator,A-power bounded operator,quasiaffine transform},
  language     = {eng},
  number       = {2},
  pages        = {139--159},
  publisher    = {Taylor & Francis},
  series       = {Linear and Multilinear Algebra},
  title        = {Ergodic properties of operators in some semi-Hilbertian spaces},
  url          = {http://dx.doi.org/10.1080/03081087.2012.667094},
  volume       = {61},
  year         = {2012},
}