Displaying similar documents to “Homogeneity and rigidity in Erdös 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.

The complemented subspace problem revisited

N. J. Kalton (2008)

Studia Mathematica

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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.

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

Artur Michalak (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic...

Proper subspaces and compatibility

Esteban Andruchow, Eduardo Chiumiento, María Eugenia Di Iorio y Lucero (2015)

Studia Mathematica

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Let 𝓔 be a Banach space contained in a Hilbert space 𝓛. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambickiĭ, we say that a bounded operator on 𝓔 is a proper operator if it admits an adjoint with respect to the inner product of 𝓛. A proper operator which is self-adjoint with respect to the inner product of 𝓛 is called symmetrizable. By a proper subspace 𝓢 we mean a closed subspace of 𝓔 which is the range of a proper projection....

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.

Nonhomogeneity of Remainders, II

A. V. Arhangel'skii, J. van Mill (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous.

A product of three projections

Eva Kopecká, Vladimír Müller (2014)

Studia Mathematica

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Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam...

Linearity in non-linear problems.

Richard Aron, Domingo García, Manuel Maestre (2001)

RACSAM

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Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.