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

Extracta Mathematicae (1996)

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

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topArranz, 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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