for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

A twisted sum Z of two Banach spaces X and Y is defined (see [11]) through a short exact sequence: 0 −→ X −→ Z −→ Y −→ 0. These short exact sequences in the category of (quasi-)Banach spaces are considered naturally in the investigation of three space properties (a property P in the category of quasi-Banach spaces is called a three space property if for every short exact sequence as above, Z ha...

We derive Banach-Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of n-homogeneous approximable polynomials on real Banach spaces E and F is induced by an isometric isomorphism of E′ onto F ′. With an additional geometric condition we obtain the analogous result in the complex case. Isometries between spaces of n-homogeneous integ...

In this paper we show that the study of integrability and D-representability of Lipschitz functions deened on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.

Homogeneous Banach spaces determined by the Jacobi translation operator are introduced and studied. Based on this translation operator a Jacobi differential operator is analyzed. Approximation procedures in the homogeneous Banach spaces are presented.

In this paper, we prove the Hyers–Ulam–Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

2. Summary of the thesis 9 2.1. Di erentiability of convex functions and the respective classes of Banach spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2. Summary of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3. Decompositions of nonseparable Banach spaces . . . . . . . . . . . . . . . 23 2.4. Summary of ...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

We study decoupling in quasi-Banach spaces. We show that decoupling is permissible in some quasi-Banach spaces (e.g., Lp and Lp/Hp when 0 < p < 1) but fails in other spaces such as the Schatten ideal Sp when 0 < p < 1. We also relate our ideas to a possible extension of the Grothendieck inequality.

This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I keep receiving requests for copies, because some of the material here does not appear elsewhere and because the Longhorn Notes are not so easy to get. Havin...