A space C(K) where all nontrivial complemented subspaces have big densities

Piotr Koszmider

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Displaying similar documents to “A space C(K) where all nontrivial complemented subspaces have big densities”

On essentially incomparable Banach spaces.

Manuel González (1991)

Extracta Mathematicae

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We introduce the concept of essentially incomparable Banach spaces, and give some examples. Then, for two essentially incomparable Banach spaces X and Y, we prove that a complemented subspace of the product X x Y is isomorphic to the product of a complemented subspace of X and a complemented subspace of Y. If, additionally, X and Y are isomorphic to their respective hyperplanes, then the group of invertible operators in X x Y is not connected. The results can be applied to some classical...

A Banach space dichotomy theorem for quotients of subspaces

Valentin Ferenczi (2007)

Studia Mathematica

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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. ...

Complemented and uncomplemented subspaces of Banach spaces.

Anatolij M. Plichko, David Yost (2000)

Extracta Mathematicae

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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.

Quotients of indecomposable Banach spaces of continuous functions

Rogério Augusto dos Santos Fajardo (2012)

Studia Mathematica

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Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where...

A continuum of totally incomparable hereditarily indecomposable Banach spaces

I. Gasparis (2002)

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A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.

Continuous restrictions of linear functionals

Béla Bollobás, Imre Leader (1992)

Acta Universitatis Carolinae. Mathematica et Physica

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c, l and l in function spaces.

Pilar Cembranos (1997)

Extracta Mathematicae

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Uncomplemented copies of C(K) inside C(K).

Francisco Arranz (1996)

Extracta Mathematicae

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Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains...

Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace

M. Ostrovskiĭ (1993)

Studia Mathematica

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The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite-dimensional subspace of X if and only if X has a nonquasireflexive quotient space with a strictly singular quotient mapping.

Primariness of some spaces of continuous functions.

Lech Drewnowski (1989)

Revista Matemática de la Universidad Complutense de Madrid

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On inessential and improjective operators.

Pietro Aiena, Manuel González (1998)

Studia Mathematica

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We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of...

Decomposable subspaces of Banach spaces.

Manuel González, Antonio Martinón (2003)

RACSAM

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We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.

On some properties of quotients of homogeneous C(K) spaces

Artur Michalak (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic...