Biorthogonal systems in certain Banach spaces.

We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.

Complex Banach spaces with Valdivia dual unit ball.

Ondrej F. K. Kalenda (2005)

Extracta Mathematicae

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We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.

On the existence of fundamental and total founded biorthogonal systems in Banach spaces

W. Davis, W. Johnson (1973)

Studia Mathematica

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Weak compact generating in duality

Kamil John, Václav Zizler (1976)

Studia Mathematica

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On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski (1995)

Studia Mathematica

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We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.