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 cer...

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, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

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 $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...