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

Previous Page 3

Displaying 41 – 57 of 57

Showing per page

Weakly continuous functions of Baire class 1.

T. S. S. R. K. Rao (2000)

Extracta Mathematicae

For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.

Weakly countably determined spaces of high complexity

Antonio Avilés (2008)

Studia Mathematica

We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity.

Weakly null sequences with upper estimates

Daniel Freeman (2008)

Studia Mathematica

We prove that if ( v i ) is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by ( v i ) , then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by ( v i ) . This extends a result of Knaust and Odell, who proved this for the cases in which ( v i ) is the standard basis for ℓ p or c₀.

Weakly uniformly rotund Banach spaces

Aníbal Moltó, Vicente Montesinos, José Orihuela, Stanimir L. Troyanski (1998)

Commentationes Mathematicae Universitatis Carolinae

The dual space of a WUR Banach space is weakly K-analytic.

Weak-star point of continuity property and Schauder bases

Ginés López-Pérez, José A. Soler-Arias (2013)

Studia Mathematica

We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we show that a dual space has the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which...

Weak-type operators and the strong fundamental lemma of real interpolation theory

N. Krugljak, Y. Sagher, P. Shvartsman (2005)

Studia Mathematica

We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the L p interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator. The inequality...

Weighted norm inequalities on spaces of homogeneous type

Qiyu Sun (1992)

Studia Mathematica

We give a characterization of the weights (u,w) for which the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w). We give a characterization of the weight functions w (respectively u) for which there exists a nontrivial u (respectively w > 0 almost everywhere) such that the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w).

Weighted spaces of holomorphic functions on Banach spaces

D. García, M. Maestre, P. Rueda (2000)

Studia Mathematica

We deal with weighted spaces H V 0 ( U ) and HV(U) of holomorphic functions defined on a balanced open subset U of a Banach space X. We give conditions on the weights to ensure that the weighted spaces of m-homogeneous polynomials constitute a Schauder decomposition for them. As an application, we study their reflexivity. We also study the existence of a predual. Several examples are provided.

Weyl numbers versus Z-Weyl numbers

Bernd Carl, Andreas Defant, Doris Planer (2014)

Studia Mathematica

Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), the s-number sequence of Z-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with Z-Weyl numbers-a problem originally posed by A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue distribution...

What is "local theory of Banach spaces"?

Albrecht Pietsch (1999)

Studia Mathematica

Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.

Wheeling around von Neumann-Jordan constant in Banach spaces

J. Alonso, P. Martín, P. L. Papini (2008)

Studia Mathematica

In recent times, many constants in Banach spaces have been defined and/or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been devoted to organize all connections, also because the literature on the subject is growing at an always bigger rate. Here we give some new connections which better the insight on some of them. In particular, we improve a known inequality between the von Neumann-Jordan and James constants.

Currently displaying 41 – 57 of 57

Previous Page 3