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In Higson and Roe's Analytic K-homology, for a unital $C*$-algebra $A$, the definitions of K-theory and K-homology have quite a similar flavor. Roughly, the group $K_0(A)$ is given by the ...

I'm trying to get an understanding of Hilbert $C^*$-bi-modules from a geometric point of view. As is well-known, we have that i) Commutative unital $C^*$-algebras correspond to compact Hausdorff ...

For $T:{\frak{Dom}}(T) \to H$ a densely defined operator, with $H$ a (separable) Hilbert space, we know that $T$ is closable if its adjoint $T^*$ has dense domain in $H$. Does this extend to the (...