All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 20 of 20

Showing per page

Cantor-Bernstein theorems for Orlicz sequence spaces

Carlos E. Finol, Marcos J. González, Marek Wójtowicz (2014)

Banach Center Publications

For two Banach spaces X and Y, we write d i m ℓ ( X ) = d i m ℓ ( Y ) if X embeds into Y and vice versa; then we say that X and Y have the same linear dimension. In this paper, we consider classes of Banach spaces with symmetric bases. We say that such a class ℱ has the Cantor-Bernstein property if for every X,Y ∈ ℱ the condition d i m ℓ ( X ) = d i m ℓ ( Y ) implies the respective bases (of X and Y) are equivalent, and hence the spaces X and Y are isomorphic. We prove (Theorems 3.1, 3.3, 3.5) that the class of Orlicz sequence spaces generated by regularly...

Cantor-Schroeder-Bernstein quadruples for Banach spaces

Elói Medina Galego (2008)

Colloquium Mathematicae

Two Banach spaces X and Y are symmetrically complemented in each other if there exists a supplement of Y in X which is isomorphic to some supplement of X in Y. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) Problem for Banach spaces by constructing two non-isomorphic Banach spaces which are symmetrically complemented in each other. In this paper, we show how to modify such a symmetry in order to ensure that X is isomorphic to Y. To do this, first we introduce the notion...

Combinatorial inequalities and subspaces of L₁

Joscha Prochno, Carsten Schütt (2012)

Studia Mathematica

Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces ℓ ⁿ M ₁ ( ℓ ⁿ M ₂ ) are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are “separated” by a function t r , 1 < r < 2.

Compactness in L¹ of a vector measure

J. M. Calabuig, S. Lajara, J. Rodríguez, E. A. Sánchez-Pérez (2014)

Studia Mathematica

We study compactness and related topological properties in the space L¹(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L¹(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration...

Complex interpolation functors with a family of quasi-power function parameters

Ming Fan (1994)

Studia Mathematica

For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters...

Compressible operators and the continuity of homomorphisms from algebras of operators

G. Willis (1995)

Studia Mathematica

The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian Banach space. The compressible operators on E form an ideal in ℬ(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.

Concerning weak * -extreme points

Eva Matoušková (1995)

Commentationes Mathematicae Universitatis Carolinae

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak * -extreme points of the unit ball is discrete.

Continuity properties up to a countable partition.

Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia (2006)

RACSAM

Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.

Countable products of spaces of finite sets

Antonio Avilés (2005)

Fundamenta Mathematicae

We consider the compact spaces σₙ(Γ) of subsets of Γ of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.

Currently displaying 1 – 20 of 20

Page 1