Uncomplemented copies of C(K) inside C(K).

Francisco Arranz

Extracta Mathematicae (1996)

  • Volume: 11, Issue: 3, page 412-413
  • ISSN: 0213-8743

Abstract

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Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains a subspace Y isomorphic to C(K) then Y contains a new subspace Z isomorphic to C(K) and complemented in X. Our aim is to obtain the uncomplemented version of Pelczynski's Theorem 1.

How to cite

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Arranz, Francisco. "Uncomplemented copies of C(K) inside C(K).." Extracta Mathematicae 11.3 (1996): 412-413. <http://eudml.org/doc/38507>.

@article{Arranz1996,
abstract = {Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains a subspace Y isomorphic to C(K) then Y contains a new subspace Z isomorphic to C(K) and complemented in X. Our aim is to obtain the uncomplemented version of Pelczynski's Theorem 1.},
author = {Arranz, Francisco},
journal = {Extracta Mathematicae},
keywords = {Espacios de Banach; Espacio de funciones continuas; Funciones continuas; Subespacios K complementados; complemented subspace; uncomplemented subspace; space; isomorphism; separable},
language = {eng},
number = {3},
pages = {412-413},
title = {Uncomplemented copies of C(K) inside C(K).},
url = {http://eudml.org/doc/38507},
volume = {11},
year = {1996},
}

TY - JOUR
AU - Arranz, Francisco
TI - Uncomplemented copies of C(K) inside C(K).
JO - Extracta Mathematicae
PY - 1996
VL - 11
IS - 3
SP - 412
EP - 413
AB - Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains a subspace Y isomorphic to C(K) then Y contains a new subspace Z isomorphic to C(K) and complemented in X. Our aim is to obtain the uncomplemented version of Pelczynski's Theorem 1.
LA - eng
KW - Espacios de Banach; Espacio de funciones continuas; Funciones continuas; Subespacios K complementados; complemented subspace; uncomplemented subspace; space; isomorphism; separable
UR - http://eudml.org/doc/38507
ER -

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