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1

A Banach space dichotomy theorem for quotients of subspaces

100%

Ferenczi V.

Studia Mathematica

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2007

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tom 180

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nr 2

111-131

EN

A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.

2

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

63%

Ferenczi V., Rosendal C.

Studia Mathematica

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2005

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tom 168

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nr 3

203-216

EN

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let 𝔛 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 𝔛, and in that case, 𝔛 is isomorphic to its square, to its hyperplanes, uniformly isomorphic to $𝔛 ⊕ [e_{i}]_{i∈D}$ for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition into uniformly isomorphic copies of itself.

3

Some strongly bounded classes of Banach spaces

63%

Dodos P., Ferenczi V.

Fundamenta Mathematicae

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2007

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tom 193

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nr 2

171-179

EN

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.

Ograniczanie wyników

2 Studia Mathematica

1 Fundamenta Mathematicae

3 Ferenczi V.

1 Dodos P.

1 Rosendal C.

2 2007

1 2005

A Banach space dichotomy theorem for quotients of subspaces

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

Some strongly bounded classes of Banach spaces