On some properties of quotients of homogeneous C(K) spaces

Artur Michalak

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Displaying similar documents to “On some properties of quotients of homogeneous C(K) spaces”

Every separable L₁-predual is complemented in a C*-algebra

Wolfgang Lusky (2004)

Studia Mathematica

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We show that every separable complex L₁-predual space X is contractively complemented in the CAR-algebra. As an application we deduce that the open unit ball of X is a bounded homogeneous symmetric domain.

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.

Uncomplemented copies of C(K) inside C(K).

Francisco Arranz (1996)

Extracta Mathematicae

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Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains...

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.

Some linear topological properties of the hardy spaces $𝐇^{p}$

S. Kwapień, A. Pelczyński (1976)

Compositio Mathematica

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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...