Extension of operators from weak*-closed sub-spaces of $l_1$ into C(K) spaces

W. Johnson; M. Zippin

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Sobczyk's theorems from A to B.

Félix Cabello Sánchez, Jesús M. Fernández Castillo, David Yost (2000)

Extracta Mathematicae

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Sobczyk's theorem is usually stated as: . Nevertheless, our understanding is not complete until we also recall: . Now the limits of the phenomenon are set: although c is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l.

Some properties of basic sequences in Banach spaces.

Manuel Valdivia (1997)

Revista Matemática de la Universidad Complutense de Madrid

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On prequojections and their duals.

M. I. Ostrovskii (1998)

Revista Matemática Complutense

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The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce...

Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace

M. Ostrovskiĭ (1993)

Studia Mathematica

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The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite-dimensional subspace of X if and only if X has a nonquasireflexive quotient space with a strictly singular quotient mapping.

Complemented and uncomplemented subspaces of Banach spaces.

Anatolij M. Plichko, David Yost (2000)

Extracta Mathematicae

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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.

The Johnson-Lindenstrauss space.

David Yost (1997)

Extracta Mathematicae

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The dual of every Asplund space admits a projectional resolution of the identity

Marián Fabian, Gilles Godefroy (1988)

Studia Mathematica

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

W. Davis, W. Johnson (1973)

Studia Mathematica

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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...

Absolutely summing operators in $ℒ_{p}$ -spaces and their applications

J. Lindenstrauss, A. Pełczyński (1968)

Studia Mathematica

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Some properties of $l_{p}$ ,0 < p < 1

W. Stiles (1972)

Studia Mathematica

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Displaying similar documents to “Extension of operators from weak*-closed sub-spaces of l 1 into C(K) spaces”

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