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The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the differentiability of these generalized inverses is studied in the context of C*-algebras.
An n-homomorphism between algebras is a linear map $phi : A to B$ such that $phi(a_1 ... a_n) = phi(a_1)... phi(a_n)$ for all elements $a_1, >..., a_n in A.$ Every homomorphism is an n-homomorphism, for all n >= 2, but the converse is false, in gener
Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.
We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{o}lners type characterizations of amenability and give an example of a semigroup whose semi
In the present paper we obtain an intrinsic characterization of real locally C*-algebras (projective limits of projective families of real C*-algebras) among complete real lmc *-algebras, and of locally JB-algebras (projective limits of projective fa
Let $G$ be a locally compact group. It is not always the case that its reduced C*-algebra $C^*_r(G)$ admits a tracial state. We exhibit closely related necessary and sufficient conditions for the existence of such. We gain a complete answer when $G$