منابع مشابه
Interpolating Hereditarily Indecomposable Banach Spaces
A Banach space X is said to be Hereditarily Indecomposable (H.I.) if for any pair of closed subspaces Y , Z of X with Y ∩ Z = {0}, Y + Z is not a closed subspace. (Throughout this section by the term “subspace” we mean a closed infinite-dimensional subspace of X .) The H.I. spaces form a new and, as we believe, fundamental class of Banach spaces. The celebrated example of a Banach space with no...
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An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.
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A famous open problem in functional analysis is whether there exists a Banach space X such that every (bounded linear) operator on X has the form λ+K where λ is a scalar and K denotes a compact operator. This problem is usually called the “scalar-plus-compact” problem [14]. One of the reasons this problem has become so attractive is that by a result of N. Aronszajn and K.T. Smith [7], if a Bana...
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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1986
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-18-1-407-417