We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

we investigate the problem of the existence of a frame forright ideals of a C*-algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*-algebraof compact operators.

Let $\mathbf{G}$ be a connected reductive group defined over locally compact non-archimedean field $F$, let $\mathbf{P}$ parabolic subgroup with Levi $\mathbf{M}$ and compatible pro-$p$ Iwahori of $G := \mathbf{G}(F)$. $R$ commutative unital ring. We introduce the Iwahori--Hecke $R$-algebra $\mathcal{H}_R(P)$ $P \mathbf{P}(F)$ construct two morphisms $\Theta^P_M\colon \mathcal{H}_R(P)\to \mathc...

background: leishmaniasis is a worldwide disease prevalent in tropical and sub- tropical countries in the world. characterization of inflammatory responses produced in cutaneous leishmaniasis has not yet been completed. methods: the specific primers were designed for ten pro-inflammatory genes including ccl4, ccl3, tnf-α, il-1α, il-12p35, il-12p40, ccl5, ccr5, il-1β and ifn- γ and their express...

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...