Displaying similar documents to “Problems on Banach spaces”

Ball remotal subspaces of Banach spaces

Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)

Colloquium Mathematicae

Similarity:

We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...

Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner (2001)

Studia Mathematica

Similarity:

Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).

Radon-Nikodým compact spaces of low weight and Banach spaces

Antonio Avilés (2005)

Studia Mathematica

Similarity:

We prove that a continuous image of a Radon-Nikodým compact of weight less than b is Radon-Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated and which has density character exactly b.

Norm attaining and numerical radius attaining operators.

María D. Acosta, Rafael Payá (1989)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result...

Composition of (E,2)-summing operators

Andreas Defant, Mieczysław Mastyło (2003)

Studia Mathematica

Similarity:

The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.

Constructing non-compact operators into c₀

Iryna Banakh, Taras Banakh (2010)

Studia Mathematica

Similarity:

We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.

Factoring Rosenthal operators.

Teresa Alvarez (1988)

Publicacions Matemàtiques

Similarity:

In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l.

Supercyclicity in the operator algebra

Alfonso Montes-Rodríguez, M. Carmen Romero-Moreno (2002)

Studia Mathematica

Similarity:

We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that...

Lineability of functionals and operators

Francisco Javier García-Pacheco, Daniele Puglisi (2010)

Studia Mathematica

Similarity:

This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show...

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

Hatamleh, Raed (2007)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94. New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.