Function spaces have essential sets

Jan Čerych

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 337-340
  • ISSN: 0010-2628

Abstract

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It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.

How to cite

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Čerych, Jan. "Function spaces have essential sets." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 337-340. <http://eudml.org/doc/248268>.

@article{Čerych1998,
abstract = {It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.},
author = {Čerych, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); its closed subspaces (called function spaces); measure orthogonal to a function algebra or to a function space; compact Hausdorff space; sup-norm algebra; function algebras; function spaces; orthogonal measure},
language = {eng},
number = {2},
pages = {337-340},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Function spaces have essential sets},
url = {http://eudml.org/doc/248268},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Čerych, Jan
TI - Function spaces have essential sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 337
EP - 340
AB - It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.
LA - eng
KW - compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); its closed subspaces (called function spaces); measure orthogonal to a function algebra or to a function space; compact Hausdorff space; sup-norm algebra; function algebras; function spaces; orthogonal measure
UR - http://eudml.org/doc/248268
ER -

References

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  1. Bear H.S., Complex function algebras, Trans. Amer. Math. Soc. 90 (1959), 383-393. (1959) Zbl0086.31602MR0107164
  2. Hoffman K., Singer I.M., Maximal algebras of continuous functions, Acta Math. 103 (1960), 217-241. (1960) Zbl0195.13903MR0117540
  3. Glicksberg I., Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 98 (1962), 415-435. (1962) Zbl0111.11801MR0173957
  4. Čerych J., On essential sets of function algebras in terms of their orthogonal measures, Comment. Math. Univ. Carolinae 36.3 (1995), 471-474. (1995) MR1364487

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