On the geometry of spaces of K-valued operators
Ehrhard Behrends (1988)
Studia Mathematica
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Ehrhard Behrends (1988)
Studia Mathematica
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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...
O. Reynov (1981)
Studia Mathematica
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H. G. Dales, W. Żelazko (2012)
Studia Mathematica
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In 1971, Grauert and Remmert proved that a commutative, complex, Noetherian Banach algebra is necessarily finite-dimensional. More precisely, they proved that a commutative, complex Banach algebra has finite dimension over ℂ whenever all the closed ideals in the algebra are (algebraically) finitely generated. In 1974, Sinclair and Tullo obtained a non-commutative version of this result. In 1978, Ferreira and Tomassini improved the result of Grauert and Remmert by showing that...
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.
Rüdiger Achilles, Mirella Manaresi (1993)
Manuscripta mathematica
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SŁawomir Solecki, Stevo Todorcevic (2004)
Annales de l’institut Fourier
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We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.
N. J. Nielsen
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W. Żelazko (1974)
Colloquium Mathematicae
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Sonia Sharma (2010)
Studia Mathematica
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We generalize an important class of Banach spaces, the M-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M-embedded operator spaces are the operator spaces which are one-sided M-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon-Nikodým property and many more, are retained in the non-commutative setting. We also discuss...
W. Żelazko (2005)
Studia Mathematica
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We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.
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........................................................
T. Banakh, M. Morayne, R. Rałowski, Sz. Żeberski (2015)
Fundamenta Mathematicae
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We study and classify topologically invariant σ-ideals with an analytic base on Euclidean spaces, and evaluate the cardinal characteristics of such ideals.
Juan Carlos Cabello Piñar (1990)
Extracta Mathematicae
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A Banach space X is an M-ideal in its bidual if the relation ||f + w|| = ||f|| + ||w|| holds for every f in X* and every w in X ⊥. The class of the Banach spaces which are M-ideals in their biduals, in short, the class of M-embedded spaces, has been carefully investigated, in particular by A. Lima, G. Godefroy and the West Berlin School. The spaces c0(I) -I any set- equipped with their canonical norm belong...
N. Hindman, D. Davenport (1987)
Semigroup forum
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Ehrhard Behrends, Peter Harmand (1985)
Studia Mathematica
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