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Displaying similar documents to “Spectrum of class w F ( p , r , q ) operators.”

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 ∈...

Spectra of partial integral operators with a kernel of three variables

Yusup Eshkabilov (2008)

Open Mathematics

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Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in C (Ω): (T 1 f)(x, y) = ∫ a b k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = ∫ c d k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra...

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.

The Słodkowski spectra and higher Shilov boundaries

Vladimír Müller (1993)

Studia Mathematica

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We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.