Displaying similar documents to “Hereditarily finitely decomposable Banach spaces”

On inessential and improjective operators.

Pietro Aiena, Manuel González (1998)

Studia Mathematica

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We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of...

Inessential operators and incomparability of Banach spaces.

Pietro Aiena, Manuel González (1991)

Extracta Mathematicae

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We obtain several characterizations for the classes of Riesz and inessential operators, and apply them to extend the family of Banach spaces for which the essential incomparability class is known, solving partially a problem posed in [6].

On essentially incomparable Banach spaces.

Manuel González (1991)

Extracta Mathematicae

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We introduce the concept of essentially incomparable Banach spaces, and give some examples. Then, for two essentially incomparable Banach spaces X and Y, we prove that a complemented subspace of the product X x Y is isomorphic to the product of a complemented subspace of X and a complemented subspace of Y. If, additionally, X and Y are isomorphic to their respective hyperplanes, then the group of invertible operators in X x Y is not connected. The results can be applied to some classical...

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...