Ergodic properties of operators in some semi-Hilbertian spaces
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2856887
- author
- Suciu, Laurian LU ; Majdak, Witold and Secelean, Nicolae
- organization
- publishing date
- 2012
- 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
- 2016-04-01 09:57:33
- date last changed
- 2022-04-19 21:15:19
@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}}, keywords = {{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}}, doi = {{10.1080/03081087.2012.667094}}, volume = {{61}}, year = {{2012}}, }