6533b86dfe1ef96bd12c9e96
RESEARCH PRODUCT
Ergodic properties of operators in some semi-Hilbertian spaces
Laurian SuciuWitold MajdakNicolae Seceleansubject
Discrete mathematicsUnbounded operatorMathematics::Dynamical SystemsAlgebra and Number TheoryNuclear operatorHilbert spaceFinite-rank operatorOperator theoryCompact operator on Hilbert spaceQuasinormal operatorsymbols.namesakesymbolsOperator normMathematicsdescription
This article deals with linear operators T on a complex Hilbert space ℋ, which are bounded with respect to the seminorm induced by a positive operator A on ℋ. 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 Cesaro ergodic, such that T * is not a quasiaffine transform of an orthogonally mean ergodic operator.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-03-29 | Linear and Multilinear Algebra |