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Displaying similar documents to “A New Hereditarily l^2 Banach Space”

Some strongly bounded classes of Banach spaces

Pandelis Dodos, Valentin Ferenczi (2007)

Fundamenta Mathematicae

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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.

Uncountable sets of unit vectors that are separated by more than 1

Tomasz Kania, Tomasz Kochanek (2016)

Studia Mathematica

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Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover...

More lr saturated L∞ spaces

Gasparis, I., Papadiamantis, M. K., Zisimopoulou, D. Z. (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 05D10, 46B03. Given r ∈ (1, ∞), we construct a new L∞ separable Banach space which is lr saturated.

Quotients of Banach spaces and surjectively universal spaces

Pandelis Dodos (2010)

Studia Mathematica

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We characterize those classes 𝓒 of separable Banach spaces for which there exists a separable Banach space Y not containing ℓ₁ and such that every space in the class 𝓒 is a quotient of Y.

Finite-dimensional decompositions of Banach spaces with (p,q)-estimates

Stanisław Prus

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CONTENTSIntroduction................................................................................................................................5I. Basic notations and definitions................................................................................................7II. Basic properties of finite-dimensional decompositions with (p,q)-estimates............................8III. A construction of f.d.d.'s satisfying (p,q)-estimates and its geometric applications...............13IV....

An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

Alistair Bird, Niels Jakob Laustsen (2010)

Banach Center Publications

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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...