Displaying similar documents to “Subspace gaps and Weyl's theorem for an elementary operator.”

Hereditarily normaloid operators.

Bhagwati Prashad Duggal (2005)

Extracta Mathematicae

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A Banach space operator T belonging to B(X) is said to be hereditarily normaloid, T ∈ HN, if every part of T is normaloid; T ∈ HN is totally hereditarily normaloid, T ∈ THN, if every invertible part of T is also normaloid; and T ∈ CHN if either T ∈ THN or T - λI is in HN for every complex number λ. Class CHN is large; it contains a number of the commonly considered classes of operators. We study operators T ∈ CHN, and prove that the Riesz projection associated with a λ ∈ isoσ(T), T ∈...

On unbounded hyponormal operators III

J. Janas (1994)

Studia Mathematica

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The paper deals mostly with spectral properties of unbounded hyponormal operators. Some nontrivial examples of such operators are given.

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...

n-supercyclic operators

Nathan S. Feldman (2002)

Studia Mathematica

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We show that there are linear operators on Hilbert space that have n-dimensional subspaces with dense orbit, but no (n-1)-dimensional subspaces with dense orbit. This leads to a new class of operators, called the n-supercyclic operators. We show that many cohyponormal operators are n-supercyclic. Furthermore, we prove that for an n-supercyclic operator, there are n circles centered at the origin such that every component of the spectrum must intersect one of these circles.

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Notes on q-deformed operators

Schôichi Ôta, Franciszek Hugon Szafraniec (2004)

Studia Mathematica

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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.

Ascent and descent for sets of operators

Derek Kitson (2009)

Studia Mathematica

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We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded operators which is compact-valued and has the projection property.

Backward Aluthge iterates of a hyponormal operator and scalar extensions

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

Studia Mathematica

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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.

On (A,m)-expansive operators

Sungeun Jung, Yoenha Kim, Eungil Ko, Ji Eun Lee (2012)

Studia Mathematica

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We give several conditions for (A,m)-expansive operators to have the single-valued extension property. We also provide some spectral properties of such operators. Moreover, we prove that the A-covariance of any (A,2)-expansive operator T ∈ ℒ(ℋ ) is positive, showing that there exists a reducing subspace ℳ on which T is (A,2)-isometric. In addition, we verify that Weyl's theorem holds for an operator T ∈ ℒ(ℋ ) provided that T is (T*T,2)-expansive. We next study (A,m)-isometric operators...