Geodesic
States which have a trace-like property relative to a C*-subalgebra of B(H)
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 158-160

Voir la notice de l'article provenant de la source Cambridge University Press

In what follows, B(H) will denote the C*-algebra of all bounded linear operators on a Hilbert space H. Suppose we are given a C*-subalgebra A of B(H), which we shall suppose contains the identity operator 1. We are concerned with the existence of states f of B(H) which satisfy the following trace-like relation relative to A:Our first result shows the existence of states f satisfying (*), when A is the C*-algebra C*(x) generated by a normaloid operator × and the identity. This allows us to give simple proofs of some well-known results in operator theory. Recall that an operator × is normaloid if its operator norm equals its spectral radius. 
Robertson, Guyan. States which have a trace-like property relative to a C*-subalgebra of B(H). Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 158-160. doi: 10.1017/S0017089500002913
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