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Assume that $B$ is a $C^{*}$ subalgebra of $A$. We say $B$ is totally non hereditary subalgebra of $A$ if not only $B$ is not a hereditary subalgebra but also it is not isomorphic to any ...

(This question was posted on MSE here but didn't get any answers.) The strict topology on the multiplier algebra M(A) of a C*-algebra A is that generated by the seminorms $$ x\mapsto \|ax\|\quad x\...

Pick a C*-algebra $A$ and call a (*-)endomorphism $\alpha:A\to A$ nontrivial if it is injective and $\alpha(A)\neq A$. Question: Do there exist infinite dimensional C*-algebras with no nontrivial ...