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 17 Next

Displaying 321 – 340 of 372

Showing per page

Analytic Renormings of C(K) Spaces

Hájek, Petr (1996)

Serdica Mathematical Journal

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit...

Another approach to characterizations of generalized triangle inequalities in normed spaces

Tamotsu Izumida, Ken-Ichi Mitani, Kichi-Suke Saito (2014)

Open Mathematics

In this paper, we consider a generalized triangle inequality of the following type: x 1 + ⋯ + x n p ⩽ x 1 p μ 1 + ⋯ + x 2 p μ n f o r a l l x 1 , ... , x n ∈ X , where (X, ‖·‖) is a normed space, (µ1, ..., µn) ∈ ℝn and p > 0. By using ψ-direct sums of Banach spaces, we present another approach to characterizations of the above inequality which is given by [Dadipour F., Moslehian M.S., Rassias J.M., Takahasi S.-E., Nonlinear Anal., 2012, 75(2), 735–741].

Answer to a question by M. Feder about K(X,Y).

G. Emmanuele (1993)

Revista Matemática de la Universidad Complutense de Madrid

We show that a Banach space constructed by Bourgain-Delbaen in 1980 answers a question put by Feder in 1982 about spaces of compact operators.

Antiproximinal sets in the Banach space c ( X )

S. Cobzaş (1997)

Commentationes Mathematicae Universitatis Carolinae

If X is a Banach space then the Banach space c ( X ) of all X -valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C ( X ) ∖ V has a nearest point in V .

Application of ( L ) sets to some classes of operators

Kamal El Fahri, Nabil Machrafi, Jawad H'michane, Aziz Elbour (2016)

Mathematica Bohemica

The paper contains some applications of the notion of Ł sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order ( L ) -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an ( L ) sets. As a sequence characterization of such operators, we see that an operator T : X → E from a Banach space into a Banach lattice is order Ł -Dunford-Pettis, if and only if | T ( x n ) | → 0 for σ ( E , E ' ) for every weakly null...

Applications of spherical designs to Banach space theory

Hermann König (2004)

Banach Center Publications

Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or ℓ p -spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants...

Currently displaying 321 – 340 of 372