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On the number of non-isomorphic subspaces of a Banach space

Valentin Ferenczi, Christian Rosendal (2005)

Studia Mathematica

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let be a Banach space with an unconditional basis ( e i ) i ∈ ℕ ; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, [ e i ] i ∈ A ≇ [ e i ] i ∈ B , or for a residual set of infinite subsets A of ℕ, [ e i ] i ∈ A is isomorphic to , and in that case, is isomorphic to its square, to its hyperplanes, uniformly isomorphic to ⊕ [ e i ] i ∈ D for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition...

On the numerical range of operators on locally and on H-locally convex spaces

Edvard Kramar (1993)

Commentationes Mathematicae Universitatis Carolinae

The spatial numerical range for a class of operators on locally convex space was studied by Giles, Joseph, Koehler and Sims in [3]. The purpose of this paper is to consider some additional properties of the numerical range on locally convex and especially on H -locally convex spaces.

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