Displaying similar documents to “Isometric embedding into spaces of continuous functions”

Uncomplemented copies of C(K) inside C(K).

Francisco Arranz (1996)

Extracta Mathematicae

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Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains...

On l^∞ subspaces of Banach spaces.

Patrick N. Dowling (2000)

Collectanea Mathematica

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We obtain refinement of a result of Partington on Banach spaces containing isomorphic copies of l-∞. Motivated by this result, we prove that Banach spaces containing asymptotically isometric copies of l-∞ must contain isometric copies of l-∞.

On the diameter of the Banach-Mazur set

Gilles Godefroy (2010)

Czechoslovak Mathematical Journal

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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.