Semi-simplicity of a proper weak -algebra.
Short Proofs of Some Structure Theorems on m-Convex Algebras
Solved and unsolved problems in generalized notions of amenability for Banach algebras
We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.
Some characterizations of complex normed Q-algebras.
Some module cohomological properties of Banach algebras
We find some relations between module biprojectivity and module biflatness of Banach algebras and and their projective tensor product . For some semigroups , we study module biprojectivity and module biflatness of semigroup algebras .
Stability of commuting maps and Lie maps
Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras...
Structure -convexe d’une algèbre limite inductive localement convexe d’algèbres de Banach
Structure of locally idempotent algebras.
Structure theory of homologically trivial and annihilator locally C*-algebras
We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C*-algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C*-algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically...
Superstability for generalized module left derivations and generalized module derivations on a Banach module. I.
Sur la transformation de Dirac d'un espace à génération compacte