Displaying similar documents to “On certain quantities in Fredholm operator theory and Mil'man's isometry spectrum”

Note on operational quantities and Mil'man isometry spectrum.

Manuel González, Antonio Martinón (1991)

Extracta Mathematicae

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Let X and Y be infinite dimensional Banach spaces and let L(X,Y) be the class of all (linear continuous) operators acting between X and Y. Mil'man [5] introduced the isometry spectrum I(T) of T ∈ L(X,Y) in the following way: I(T) = {α ≥ 0: ∀ ε > 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | < ε}}, where S∞(X) is the set of all infinite dimensional closed subspaces of X and S...

On inessential and improjective operators.

Pietro Aiena, Manuel González (1998)

Studia Mathematica

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We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of...

Inessential operators and incomparability of Banach spaces.

Pietro Aiena, Manuel González (1991)

Extracta Mathematicae

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We obtain several characterizations for the classes of Riesz and inessential operators, and apply them to extend the family of Banach spaces for which the essential incomparability class is known, solving partially a problem posed in [6].

Banach spaces with small Calkin algebras

Manuel González (2007)

Banach Center Publications

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Let X be a Banach space. Let 𝓐(X) be a closed ideal in the algebra ℒ(X) of the operators acting on X. We say that ℒ(X)/𝓐(X) is a Calkin algebra whenever the Fredholm operators on X coincide with the operators whose class in ℒ(X)/𝓐(X) is invertible. Among other examples, we have the cases in which 𝓐(X) is the ideal of compact, strictly singular, strictly cosingular and inessential operators, and some other ideals introduced as perturbation classes in Fredholm theory. Our aim is to...