The kh-socle of a commutative semisimple Banach algebra

Youness Hadder

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 4, page 387-399
  • ISSN: 0862-7959

Abstract

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Let 𝒜 be a commutative complex semisimple Banach algebra. Denote by kh ( soc ( 𝒜 ) ) the kernel of the hull of the socle of 𝒜 . In this work we give some new characterizations of this ideal in terms of minimal idempotents in 𝒜 . This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.

How to cite

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Hadder, Youness. "The kh-socle of a commutative semisimple Banach algebra." Mathematica Bohemica 145.4 (2020): 387-399. <http://eudml.org/doc/297276>.

@article{Hadder2020,
abstract = {Let $\mathcal \{A\}$ be a commutative complex semisimple Banach algebra. Denote by $\{\rm kh\}(\{\rm soc\}(\mathcal \{A\}))$ the kernel of the hull of the socle of $\mathcal \{A\}$. In this work we give some new characterizations of this ideal in terms of minimal idempotents in $\mathcal \{A\}$. This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.},
author = {Hadder, Youness},
journal = {Mathematica Bohemica},
keywords = {commutative Banach algebra; socle; kh-socle; inessential element},
language = {eng},
number = {4},
pages = {387-399},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The kh-socle of a commutative semisimple Banach algebra},
url = {http://eudml.org/doc/297276},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Hadder, Youness
TI - The kh-socle of a commutative semisimple Banach algebra
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 4
SP - 387
EP - 399
AB - Let $\mathcal {A}$ be a commutative complex semisimple Banach algebra. Denote by ${\rm kh}({\rm soc}(\mathcal {A}))$ the kernel of the hull of the socle of $\mathcal {A}$. In this work we give some new characterizations of this ideal in terms of minimal idempotents in $\mathcal {A}$. This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.
LA - eng
KW - commutative Banach algebra; socle; kh-socle; inessential element
UR - http://eudml.org/doc/297276
ER -

References

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