Sin-ei Takahasi

Equivalent conditions for the general Stone-Weierstrass problem

We generalize the setting of the Stone-Weierstrass problem to the cone CP(A, H) of all completely positive linear maps of a C*-algebra A into the C*-algebra B(H) of all bounded linear operators on a Hilbert space H, and give some equivalent conditions for the problem. As a consequence, a new generalized spectrum, containing pure states and irreducible representations, will be introduced.

Remarks on quasicentral approximate identities

We give a new interpretation of the theorem of Doran and Wichmann concerning quasicentral approximate identities and their applications.