Segal extensions and Segal algebras in uniform Banach algebras

2021 ◽  
Author(s):  
Subhash J. Bhatt ◽  
Prakash A. Dabhi
Keyword(s):  
Banach Algebras ◽  
Segal Algebras

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.

scholarly journals Constructions of the maximal strongly character invariant segal algebras and their applications

1983 ◽  
Vol 35 (1) ◽  
pp. 123-131
Author(s):  
Chang-Pao Chen
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Banach Algebras ◽  
Dual Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Segal Algebra ◽  
Segal Algebras

AbstractLet G denote any locally compact abelian group with the dual group Γ. We construct a new kind of subalgebra L1(G) ⊗ΓS of L1(G) from given Banach ideal S of L1(G). We show that L1(G) ⊗гS is the larger amoung all strongly character invariant homogeneous Banach algebras in S. when S contains a strongly character invariant Segal algebra on G, it is show that L1(G) ⊗гS is also the largest among all strongly character invariant Segal algebras in S. We give applications to characterizations of two kinds of subalgebras of L1(G)-strongly character invariant Segal algebras on G and Banach ideal in L1(G) which contain a strongly character invariant Segal algebra on G.

scholarly journals Closed subalgebras of homogeneous Banach algebras

1975 ◽  
Vol 20 (3) ◽  
pp. 366-376 ◽  
Author(s):  
Ching-Nan Tseng ◽  
Hawi-Chiuan Wang
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Banach Algebras ◽  
Synthesis Method ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Closed Subalgebras ◽  
Segal Algebras

AbstractRudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.

Weak amenability of certain classes of Banach algebras without bounded approximate identities

2002 ◽  
Vol 133 (2) ◽  
pp. 357-371 ◽  
Author(s):  
F. GHAHRAMANI ◽  
A. T. M. LAU
Keyword(s):  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Segal Algebra ◽  
Weak Amenability ◽  
Approximate Identities ◽  
Dual Module ◽  
Arens Regularity ◽  
Segal Algebras

In a recent paper [3] Dales and Pandey have shown that the class Sp of Segal algebras is weakly amenable. In this paper, for various classes of Segal algebras, we characterize derivations and multipliers from a Segal algebra into itself and into its dual module. In particular, we prove that every Segal algebra on a locally compact abelian group is weakly amenable and an abstract Segal subalgebra of a commutative weakly amenable Banach algebra is weakly amenable. We also introduce the Lebesgue–Fourier algebra of a locally compact group G and study its Arens regularity when G is discrete or compact.

scholarly journals Segal algebras in commutative Banach algebras

2014 ◽  
Vol 44 (2) ◽  
pp. 539-589 ◽  
Author(s):  
Jyunji Inoue ◽  
Sin-Ei Takahasi
Keyword(s):  
Banach Algebras ◽  
Commutative Banach Algebras ◽  
Segal Algebras
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