Processing math: 0%

Wykorzystujemy pliki cookies aby ułatwić Ci korzystanie ze strony oraz w celach analityczno-statystycznych.

A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Complementations in and \ell _\infty (X)

Volume 172 / 2023

Leandro Candido Colloquium Mathematicum 172 (2023), 129-141 MSC: Primary 46E40; Secondary 46E15, 46B25, 46A45. DOI: 10.4064/cm8868-10-2022 Published online: 14 November 2022

Abstract

We investigate the geometry of C(K,X) and \ell _{\infty }(X) spaces through complemented subspaces of the form (\bigoplus _{i\in \varGamma }X_i)_{c_0}. For Banach spaces X and Y, we prove that if \ell _{\infty }(X) has a complemented subspace isomorphic to c_0(Y), then, for some n \in \mathbb N , X^n has a subspace isomorphic to c_0(Y). If K and L are Hausdorff compact spaces and X and Y are Banach spaces having no subspace isomorphic to c_0 we further prove the following:

(1) If C(K)\sim c_0(C(K)) and C(L)\sim c_0(C(L)) and \ell _{\infty }(C(K,X))\sim \ell _{\infty }(C(L,Y)), then K and L have the same cardinality.

(2) If K and L are infinite and metrizable and \ell _{\infty }(C(K,X))\sim \ell _{\infty }(C(L,Y)), then C(K) is isomorphic to C(L).

Authors

  • Leandro CandidoDepartamento de Matemática
    Instituto de Ciência e Tecnologia
    Universidade Federal de São Paulo – UNIFESP
    São José dos Campos, SP, Brasil
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image