Displaying similar documents to “Remarks on rich subspaces of Banach spaces”

On interpolation of tensor products of Banach spaces.

Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)

RACSAM

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For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.

Subspaces with a common complement in a Banach space

Dimosthenis Drivaliaris, Nikos Yannakakis (2007)

Studia Mathematica

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We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an...

Estimates for projections in Banach spaces and existence of direct complements

Gunther Dirr, Vladimir Rakočević, Harald K. Wimmer (2005)

Studia Mathematica

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Let W and L be complementary subspaces of a Banach space X and let P(W,L) denote the projection on W along L. We obtain a sufficient condition for a subspace M of X to be complementary to W and we derive estimates for the norm of P(W,L) - P(W,M).

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...

Quotients of Banach Spaces with the Daugavet Property

Vladimir Kadets, Varvara Shepelska, Dirk Werner (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.