Displaying similar documents to “Operators of the q-oscillator”

Notes on q-deformed operators

Schôichi Ôta, Franciszek Hugon Szafraniec (2004)

Studia Mathematica

Similarity:

The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.

On λ-commuting operators

John B. Conway, Gabriel Prǎjiturǎ (2005)

Studia Mathematica

Similarity:

For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.

Backward extensions of hyperexpansive operators

Zenon J. Jabłoński, Il Bong Jung, Jan Stochel (2006)

Studia Mathematica

Similarity:

The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.

Polaroid type operators and compact perturbations

Chun Guang Li, Ting Ting Zhou (2014)

Studia Mathematica

Similarity:

A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property...

Compact operators between K- and J-spaces

Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez (2005)

Studia Mathematica

Similarity:

The paper establishes necessary and sufficient conditions for compactness of operators acting between general K-spaces, general J-spaces and operators acting from a J-space into a K-space. Applications to interpolation of compact operators are also given.

Backward Aluthge iterates of a hyponormal operator and scalar extensions

C. Benhida, E. H. Zerouali (2009)

Studia Mathematica

Similarity:

Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.