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.

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

These are notes for a lecture delivered on 12 May, 2008, in a graduate course on operator algebras in Berkeley. The intent was to give a brief introduction to the basic ideas of operator space theory. The notes were hastily written and have not been carefully checked for accuracy or political correctness. 1. An overview of operator spaces We learn early on that every Banach space S is isometric...

1. Apologies. Since much of the recent work in the Banach space aspects of Functional Analysis, especially the geometry of Banach spaces, could, by a bit of chicanery, be construed as applications of Banach ideals, the title does not indicate a complete survey. This work is surely not exhaustive of the subject matter. Thus, many good papers are totally ignored. This is somewhat compensated for ...

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.

In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every n-linear mapping from L∞-spaces into K is (2; 2, ..., 2,∞)-summing and also shown that every n-linear mapping from L∞-spaces into F is (q; 2, ..., 2)-summing whenever F has cotype q. We also give new examples of analytic summing mappings and polynomial...

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.