Displaying similar documents to “Invariant subspaces of X * * under the action of biconjugates”

w * -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

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We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ ( X , Y ) is not reflexive for reflexive X and Y then ℒ ( X 1 , Y ) is is not reflexive for some X 1 ⊂ X , X 1 having a basis.

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.

On decompositions of Banach spaces into a sum of operator ranges

V. Fonf, V. Shevchik (1999)

Studia Mathematica

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It is proved that a separable Banach space X admits a representation X = X 1 + X 2 as a sum (not necessarily direct) of two infinite-codimensional closed subspaces X 1 and X 2 if and only if it admits a representation X = A 1 ( Y 1 ) + A 2 ( Y 2 ) as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation X = T 1 ( Z 1 ) + T 2 ( Z 2 ) such that neither of the operator ranges T 1 ( Z 1 ) , T 2 ( Z 2 ) contains an infinite-dimensional closed subspace...