Topological algebras with an orthogonal total sequence

Hermann Render

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 2, page 215-222
  • ISSN: 0010-1354

Abstract

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The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the “coefficient functionals”. Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence ( x n ) n ∈ ℕ satisfying x n 2 = x n and x n x n + 1 = x n + 1 for all n ∈ ℕ.

How to cite

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Render, Hermann. "Topological algebras with an orthogonal total sequence." Colloquium Mathematicae 72.2 (1997): 215-222. <http://eudml.org/doc/210460>.

@article{Render1997,
abstract = {The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the “coefficient functionals”. Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence $(x_n)_\{n∈ℕ\}$ satisfying $x^2_n=x_n$ and $x_n x_\{n+1\} = x_\{n+1\}$ for all n ∈ ℕ.},
author = {Render, Hermann},
journal = {Colloquium Mathematicae},
keywords = {orthogonal basis; Hadamard product; topological algebra; closed prime ideals; coefficient functionals; topological algebras; closed maximal ideals; kernels of multiplicative functionals; orthogonal total sequence; unital Fréchet algebra; Schauder basis},
language = {eng},
number = {2},
pages = {215-222},
title = {Topological algebras with an orthogonal total sequence},
url = {http://eudml.org/doc/210460},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Render, Hermann
TI - Topological algebras with an orthogonal total sequence
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 2
SP - 215
EP - 222
AB - The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the “coefficient functionals”. Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence $(x_n)_{n∈ℕ}$ satisfying $x^2_n=x_n$ and $x_n x_{n+1} = x_{n+1}$ for all n ∈ ℕ.
LA - eng
KW - orthogonal basis; Hadamard product; topological algebra; closed prime ideals; coefficient functionals; topological algebras; closed maximal ideals; kernels of multiplicative functionals; orthogonal total sequence; unital Fréchet algebra; Schauder basis
UR - http://eudml.org/doc/210460
ER -

References

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  13. [13] H. Render and A. Sauer, Algebras of holomorphic functions with Hadamard multiplication, Studia Math. 118 (1996), 77-100. Zbl0855.46032
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