Displaying similar documents to “On the Kunen-Shelah properties in Banach spaces”

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.

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...

Constructing non-compact operators into c₀

Iryna Banakh, Taras Banakh (2010)

Studia Mathematica

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We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.

Domination by positive Banach-Saks operators

Julio Flores, César Ruiz (2006)

Studia Mathematica

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Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.

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.

Kadec Norms on Spaces of Continuous Functions

Burke, Maxim R., Wiesaw, Kubis, Stevo, Todorcevic (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35. We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing...

Commutators in Banach *-algebras

Bertram Yood (2008)

Studia Mathematica

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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.