Displaying similar documents to “Bounded and unbounded operators between Köthe spaces”

On λ-commuting operators

John B. Conway, Gabriel Prǎjiturǎ (2005)

Studia Mathematica

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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.

Factorization of unbounded operators on Köthe spaces

T. Terzioğlu, M. Yurdakul, V. Zahariuta (2004)

Studia Mathematica

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The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means...

Compact operators between K- and J-spaces

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

Studia Mathematica

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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 extensions of hyperexpansive operators

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

Studia Mathematica

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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.

Disjoint hypercyclic operators

Luis Bernal-González (2007)

Studia Mathematica

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We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.

Polaroid type operators and compact perturbations

Chun Guang Li, Ting Ting Zhou (2014)

Studia Mathematica

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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...