In [9], Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras. In particular, we prove that tsr(A) ≥ t...

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,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian ∗-alg...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...