Displaying similar documents to “Quotients of indecomposable Banach spaces of continuous functions”

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.

A weakly chainable uniquely arcwise connected continuum without the fixed point property

Mirosław Sobolewski (2015)

Fundamenta Mathematicae

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A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.

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. ...