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Displaying similar documents to “Continuous dependence on parameters of the fixed points set for some set-valued operators”

A generalization of a theorem of Mammana

Roberto Camporesi, Antonio J. Di Scala (2011)

Colloquium Mathematicae

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We prove that any linear ordinary differential operator with complex-valued coefficients continuous in an interval I can be factored into a product of first-order operators globally defined on I. This generalizes a theorem of Mammana for the case of real-valued coefficients.

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...

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.

Approximation of set-valued functions with compact images-an overview

Nira Dyn, Elza Farkhi (2006)

Banach Center Publications

Similarity:

Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing degree, and the Schoenberg operators, when represented as spline subdivision schemes, converge...