Equicontinuity of power maps in locally pseudo-convex algebras

Abdellah El Kinani

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 1, page 91-98
  • ISSN: 0010-2628

Abstract

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We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.

How to cite

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El Kinani, Abdellah. "Equicontinuity of power maps in locally pseudo-convex algebras." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 91-98. <http://eudml.org/doc/249208>.

@article{ElKinani2003,
abstract = {We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.},
author = {El Kinani, Abdellah},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally pseudo-convex algebra; continuous product; $m$-$p$-convexity; Baire space; power maps; power maps; locally pseudoconvex algebra},
language = {eng},
number = {1},
pages = {91-98},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Equicontinuity of power maps in locally pseudo-convex algebras},
url = {http://eudml.org/doc/249208},
volume = {44},
year = {2003},
}

TY - JOUR
AU - El Kinani, Abdellah
TI - Equicontinuity of power maps in locally pseudo-convex algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 91
EP - 98
AB - We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.
LA - eng
KW - locally pseudo-convex algebra; continuous product; $m$-$p$-convexity; Baire space; power maps; power maps; locally pseudoconvex algebra
UR - http://eudml.org/doc/249208
ER -

References

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  12. Turpin P., Une remarque sur les algèbres à inverse continu, C.R. Acad. Sci. Paris, t. 270, Série A (1970), 1686-1689. Zbl0195.13804MR0268674
  13. Waelbroeck L., Topological Vector Spaces and Algebras, Lecture Notes in Math. 230, Springer, 1971. Zbl0225.46001MR0467234
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