Displaying similar documents to “Equilateral sets in Banach spaces of the form C(K)”

More lr saturated L∞ spaces

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

Serdica Mathematical Journal

Similarity:

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

Convex sets in Banach spaces and a problem of Rolewicz

A. Granero, M. Jiménez Sevilla, J. Moreno (1998)

Studia Mathematica

Similarity:

Let B x be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of B x and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).

Kadec Norms on Spaces of Continuous Functions

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

Serdica Mathematical Journal

Similarity:

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...

Quotients of Banach spaces and surjectively universal spaces

Pandelis Dodos (2010)

Studia Mathematica

Similarity:

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.

On the diameter of the Banach-Mazur set

Gilles Godefroy (2010)

Czechoslovak Mathematical Journal

Similarity:

On every subspace of l ∞ ( ℕ ) which contains an uncountable ω -independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin’s Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of l ∞ ( ℕ ) is infinite. This provides a partial answer to a question asked by Johnson and Odell.

Constructing non-compact operators into c₀

Iryna Banakh, Taras Banakh (2010)

Studia Mathematica

Similarity:

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.