In this paper, we study approximate identity properties, some propositions from Baker, Dales, Lau in general situations and establish relationships between the topological centers of module actions factorization properties with results group algebras. We consider under which sufficient necessary conditions Banach algebra $A\widehat{\otimes}B$ is Arens regular.

We prove that if X is a locally compact σ-compact space then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if X is second countable locally compact then γ(X) is second countable locally compact Hausdorff if and only i...

We discuss Arens regularity of the projective tensor product Banach algebras consisting Schatten class operators. More precisely, exploiting Ülger’s biregularity criterion, we prove that for any Hilbert space ℋ, Sp(ℋ)⊗γ Sq (ℋ) and B(S2(ℋ))⊗γ S2(ℋ) are not regular every pair 1≤p,q≤2; whereas, when ℋ is separable equipped with Schur product, show completely continuous S2(ℋ)⊗γ regular.

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of ...

For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A∗ of A∗. The class of dual Banach algebras includes all W ∗-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception...

An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexi...

Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...