On some subspaces of the Helly space
W. F. Pfeffer (1976)
Colloquium Mathematicae
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Displaying similar documents to “Proper subspaces and compatibility”
On some subspaces of the Helly space
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Quotients of Banach Spaces with the Daugavet Property
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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.
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Jaroslav Milota (1976)
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Banach spaces all of whose subspaces have the approximation property
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We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-1))-isomorphic to a Hilbert space, where C is an absolute constant; this estimate (up to the constant C) is best possible. This answers a question of Kadets and Mityagin from 1973. We also investigate the finite-dimensional versions of the theorem.
Subspaces with a common complement in a Banach space
Dimosthenis Drivaliaris, Nikos Yannakakis (2007)
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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...
On property in -spaces
Józef Burzyk, Andrzej Kamiński (1999)
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