Symmetric Segal algebras on compact groups

Author(s):  
Hans Reiter
2011 ◽  
Vol 86 (1) ◽  
pp. 90-99 ◽  
Author(s):  
ZEINAB KAMALI ◽  
MEHDI NEMATI

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.


2009 ◽  
Vol 79 (2) ◽  
pp. 319-325 ◽  
Author(s):  
H. SAMEA

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.


2013 ◽  
Vol 95 (1) ◽  
pp. 20-35 ◽  
Author(s):  
MAHMOOD ALAGHMANDAN

AbstractIn this paper we first show that for a locally compact amenable group $G$, every proper abstract Segal algebra of the Fourier algebra on $G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact abelian group is not approximately amenable. Then using the hypergroup generated by the dual of a compact group, it is shown that all proper Segal algebras of a class of compact groups including the $2\times 2$ special unitary group, $\mathrm{SU} (2)$, are not approximately amenable.


1982 ◽  
Vol 25 (3) ◽  
pp. 441-451
Author(s):  
U.B. Tewari ◽  
K. Parthasarathy

Let G1, G2, be locally compact groups and let S1, S2, be Segal algebras on G1, G2, respectively. Under certain conditions on G1, G2, and S1, S2, we prove that if there is a bipositive or isometric isomorphism between S1, S2, or between their multiplier algebras then G1, and G2, are topologically isomorphic.


2010 ◽  
Vol 82 (2) ◽  
pp. 274-281 ◽  
Author(s):  
MAHMOOD ALAGHMANDAN ◽  
RASOUL NASR-ISFAHANI ◽  
MEHDI NEMATI

AbstractLet ℬ be an abstract Segal algebra with respect to 𝒜. For a nonzero character ϕ on 𝒜, we study ϕ-amenability, and ϕ-contractibility of 𝒜 and ℬ. We then apply these results to abstract Segal algebras related to locally compact groups.


2017 ◽  
Vol 67 (1) ◽  
pp. 191-198
Author(s):  
Rasoul Nasr-Isfahani ◽  
Mehdi Nemati ◽  
Sima Soltani Renani

Abstract We study projectivity and injectivity for Banach modules over abstract Segal algebras. We then apply these results to abstract Segal algebras related to locally compact groups.


2010 ◽  
Vol 106 (2) ◽  
pp. 243 ◽  
Author(s):  
H. Samea

In this paper the approximate weak amenability of abstract Segal algebras is investigated. Applications to compact groups are given. Also an open problem raised by Ghahramani and Lau is answered negatively.


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