A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated With Locally Compact Groups

2021 ◽  
Author(s):  
Anthony To-Ming Lau ◽  
Ali ÜLger
Keyword(s):  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Bounded Operators ◽  
Unified Approach ◽  
Locally Compact ◽  
Topological Center ◽  
Power Bounded Operators ◽  
Arens Regularity ◽  
Power Bounded

Abstract Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.

scholarly journals ON THE TOPOLOGICAL CENTRE OF L1(G/H)**

2012 ◽  
Vol 86 (1) ◽  
pp. 119-125 ◽  
Author(s):  
R. RAISI TOUSI ◽  
R. A. KAMYABI-GOL ◽  
H. R. EBRAHIMI VISHKI
Keyword(s):  
Compact Group ◽  
Banach Algebras ◽  
Compact Subgroup ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
General Criterion ◽  
Unified Approach ◽  
Locally Compact ◽  
Topological Centre

AbstractLet G be a locally compact group and H be a compact subgroup of G. Using a general criterion established by Neufang [‘A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis’, Arch. Math.82(2) (2004), 164–171], we show that the Banach algebra L1(G/H) is strongly Arens irregular for a large class of locally compact groups.

scholarly journals THE MODULUS OF WEAKLY COMPACT MULTIPLIERS ON THE BANACH ALGEBRA L1(𝒢)** OF A LOCALLY COMPACT GROUP

2012 ◽  
Vol 86 (2) ◽  
pp. 315-321
Author(s):  
MOHAMMAD JAVAD MEHDIPOUR
Keyword(s):  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Locally Compact ◽  
Weakly Compact ◽  
Necessary And Sufficient ◽  
Funct Anal

AbstractIn this paper we give a necessary and sufficient condition under which the answer to the open problem raised by Ghahramani and Lau (‘Multipliers and modulus on Banach algebras related to locally compact groups’, J. Funct. Anal. 150 (1997), 478–497) is positive.

scholarly journals ON n-IDEAL AMENABILITY OF CERTAIN BANACH ALGEBRAS

2011 ◽  
Vol 86 (1) ◽  
pp. 90-99 ◽  
Author(s):  
ZEINAB KAMALI ◽  
MEHDI NEMATI
Keyword(s):  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Ideal Amenability ◽  
Segal Algebras

AbstractIn this paper we consider some notions of amenability such as ideal amenability, n-ideal amenability and approximate n-ideal amenability. The first two were introduced and studied by Gordji, Yazdanpanah and Memarbashi. We investigate some properties of certain Banach algebras in each of these classes. Results are also given for Segal algebras on locally compact groups.

scholarly journals ESSENTIAL AMENABILITY OF ABSTRACT SEGAL ALGEBRAS

2009 ◽  
Vol 79 (2) ◽  
pp. 319-325 ◽  
Author(s):  
H. SAMEA
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Segal Algebra ◽  
Amenable Banach Algebra ◽  
Segal Algebras

AbstractA number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.

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