Ergodic properties of operators in some semi-Hilbertian spaces

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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.

Detaljer

Författare
  • Laurian Suciu
  • Witold Majdak
  • Nicolae Secelean
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)139-159
TidskriftLinear and Multilinear Algebra
Volym61
Utgåva nummer2
StatusPublished - 2012
PublikationskategoriForskning
Peer review utfördJa