N ov 1 99 9 ON SUBSPACES OF c 0 AND EXTENSION OF OPERATORS INTO C ( K ) - SPACES
نویسندگان
چکیده
Johnson and Zippin recently showed that ifX is a weak∗-closed subspace of l1 and T : X → C(K) is any bounded operator then T can extended to a bounded operator T̃ : l1 → C(K). We give a converse result: if X is a subspace of l1 so that l1/X has a (UFDD) and every operator T : X → C(K) can be extended to l1 then there is an automorphism τ of l1 so that τ(X) is weak∗-closed. This result is proved by studying subspaces of c0 and several different characterizations of such subspaces are given.
منابع مشابه
Extension of linear operators and Lipschitz maps into C(K)-spaces
We study the extension of linear operators with range in a C(K)space, comparing and contrasting our results with the corresponding results for the nonlinear problem of extending Lipschitz maps with values in a C(K)space. We give necessary and sufficient conditions on a separable Banach space X which ensure that every operator T : E → C(K) defined on a subspace may be extended to an operator e T...
متن کاملTHE ROPER-SUFFRIDGE EXTENSION OPERATORS ON THE CLASS OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE $beta$ AND ORDER $alpha$
Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...
متن کاملOn the Extension of Operators with Range in a C(k) Space
Theorem. For X= C(K) the following four statements are equivalent. (i) For every two Banach spaces ZD Y with dim(Z/ Y) = 1 and every operator T from Y into X with a separable range there is an extension T of T from Z into X with \\t\\=\\T\\. •J J 11 11 11 M (ii) For every two Banach spaces ZZ)Y with dim Y =2, dim Z = 3 and every operator T from Y into X there is an extension f of T from Z into ...
متن کاملFunctors Induced by Cauchy Extension of C$^ast$-algebras
In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...
متن کاملar X iv : m at h . O A / 9 80 40 64 v 1 14 A pr 1 99 8 THE COMPLETE SEPARABLE EXTENSION PROPERTY
This work introduces operator space analogues of the Separable Extension Property (SEP) for Banach spaces; the Complete Separable Extension Property (CSEP) and the Complete Separable Complemention Property (CSCP). The results use the technique of a new proof of Sobczyk’s Theorem, which also yields new results for the SEP in the non-separable situation, e.g., (⊕∞ n=1 Zn)c0 has the (2 + ε)-SEP fo...
متن کامل