Displaying similar documents to “Some ideals of operators on Hilbert space”

Finite representability and super-ideals of operators

Stefan Heinrich

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CONTENTSIntroduction............................................................................... 5Notation............................................................................................. 61. Finite representability of operators.......................................... 72. Super-ideals of operators......................................................... 143. Connections with Banach space theory................................. 204. Procedures on super-ideals........................................................

Absolutely (r,p,q)-summing inclusions

Carsten Michels (2007)

Studia Mathematica

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As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between...

The history of a general criterium on spaceability

Víctor M. Sánchez (2017)

Open Mathematics

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There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F) I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general...

Structural properties of ideals

J. E. Baumgartner, A. D. Taylor, S. Wagon

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CONTENTSPreface.............................................................................................. 5Chapter I. Preliminaries................................................................. 61. Notation and terminology.......................................................... 62. Results from the literature......................................................... 93. Definitions and basic properties.............................................. 11Chapter II. Subnormality and...

Combinatorics of ideals --- selectivity versus density

A. Kwela, P. Zakrzewski (2017)

Commentationes Mathematicae Universitatis Carolinae

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This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.