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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 57: Issue 3
DOI:
https://doi.org/10.1556/012.2020.57.3.1465
Authors:
Abdullah Alahmari
,
Falih A. Aldosray
, and
Mohamed Mabrouk

1. Introduction and preliminaries Let 𝔄 be a complex Banach algebra with unit 1 and Jacobson radical ℜ . Recall that ℜ coincides with the intersection of the maximal modular left (right) ideals, with ℜ = 𝔄 if there are no such (and then

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Acta Mathematica Hungarica
Volume/Issue:
Volume 134: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-011-0133-z
Authors:
Z. Alizadeh
,
M. Eshaghi Gordji
, and
H. Khodaei

] Eshaghi Gordgi , M. and Ghobadipour , N. , Hyers–Ulam–Aoki–Rassias stability and Ulam–Gǎvruta–Rassias stability of the quadratic homomorphisms and quadratic derivations on Banach algebras , Nova Science Publishers, Inc. ( 2010 ), 978

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 45: Issue 1
DOI:
https://doi.org/10.1556/sscmath.2007.1038
Author:
Mina Ettefagh

Let A be a Banach algebra and ( A ″, □) be its second dual with first Arens product. The third dual of A can be regarded as dual of A ″ ( A ‴ = ( A ″)′) or as the second dual of A ′ ( A ‴ = ( A ′)″), so there are two ( A ″, □)-bimodule structures on A ‴ that are not always equal. This paper determines the conditions that make these structures equal. As a consequence, there are some relations between weak amenability of A and ( A ″, □).

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 44: Issue 3
DOI:
https://doi.org/10.1556/sscmath.2007.1025
Authors:
Mahmoud Bami
and
Hojatollah Samea

In the present paper we have introduced Banach algebras \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\ell ^p - \oplus _{i \in I} \mathfrak{A}_i $$ \end{document} (1 ≦ p < ∞) of unital Banach algebras \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{A}_i ,\mathcal{M}_\infty ^0 (\mathfrak{A},I)$$ \end{document} , and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{M}^0 (\mathfrak{A},I)$$ \end{document} , in order to investigate the amenability and essential amenability of the Banach algebras \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{E}_p (I)$$ \end{document} (1 ≦ p < ∞), the convolution Banach algebra A ( G ) of a compact group G , and the ℓ 1 -Munn algebra \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{M}_I (\mathfrak{A})$$ \end{document} . Examples are given to establish negatively parts of the open problems raised by Ghahramani and Loy concerning the essential amenability of Banach algebras. Examples of semigroups S are given to prove that the amenability of S is neither sufficient nor necessary for the essential amenability of the semigroup algebra ℓ 1 ( S ).

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Acta Mathematica Hungarica
Volume/Issue:
Volume 127: Issue 3
DOI:
https://doi.org/10.1007/s10474-010-9117-7
Authors:
M. Mehdipour
and
R. Nasr-Isfahani

Abstract  

We study weakly compact left and right multipliers on the Banach algebra L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)* of a locally compact group
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
. We prove that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
is compact if and only if L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)* has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)*. We also give a description of weakly compact multipliers on L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)* in terms of weakly completely continuous elements of L 0 t8(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)*. Finally we show that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
is finite if and only if there exists a multiplicative linear functional n on L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
) such that n is a weakly completely continuous element of L 0 ∞(
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
)*
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Acta Mathematica Hungarica
Volume/Issue:
Volume 114: Issue 3
DOI:
https://doi.org/10.1007/s10474-006-0524-8
Authors:
J. Arhippainen
and
V. Müller

Abstract  

Let A be an algebra without unit. If ∥ ∥ is a complete regular norm on A it is known that among the regular extensions of ∥ ∥ to the unitization of A there exists a minimal (operator extension) and maximal (ℓ1-extension) which are known to be equivalent. We shall show that the best upper bound for the ratio of these two extensions is exactly 3. This improves the results represented by A. K. Gaur and Z. V. Kovřk and later by T. W. Palmer.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 52: Issue 3-4
DOI:
https://doi.org/10.1007/bf01951571
Author:
B. Tomiuk
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Acta Mathematica Hungarica
Volume/Issue:
Volume 42: Issue 1-2
DOI:
https://doi.org/10.1007/bf01960548
Author:
D. Petz
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Acta Mathematica Hungarica
Volume/Issue:
Volume 7: Issue 2
DOI:
https://doi.org/10.1007/bf02028204
Author:
A. Prékopa
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Acta Mathematica Hungarica
Volume/Issue:
Volume 68: Issue 1-2
DOI:
https://doi.org/10.1007/bf01874436
Authors:
Dang Vu Giang
and
Ferenc Móricz
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