Displaying similar documents to “s-Numbers of operators in Banach spaces”

On linear operators having supercyclic vectors

Gerd Herzog (1992)

Studia Mathematica

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We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.

On weakly infinite-dimensional subspuees

P. Borst (1992)

Fundamenta Mathematicae

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We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and d i m Y = ω 0 and d i m X = ω 0 + 1 . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

What is "local theory of Banach spaces"?

Albrecht Pietsch (1999)

Studia Mathematica

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Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.