Let a compact group U act by automorphisms of a commutative regular and Wiener Banach algebra A. We study representations Ru of U on quotient spaces A/I(üj), where u> is an orbit of U in the Gelfand space X of A and L(uj) is the minimal closed ideal with hull w C X. The main result of the paper is: if A = AP(X) is a weighted Fourier algebra on a LCA group X = A with a subpolynomial weight p on ...

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is dened. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...

Let A be a complex Banach algebra. If the spectrum of an invertible element a ∈ A does not separate the plane, then a admits a logarithm. We present two elementary proofs of this classical result which are independent of the holomorphic functional calculus. We also discuss the case of real Banach algebras. As applications, we obtain simple proofs that every invertible matrix over C has a logari...

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.

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.