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States which have a trace-like property relative to a C*-subalgebra of B(H)

Published online by Cambridge University Press:  18 May 2009

Guyan Robertson
Guyan Robertson
Affiliation:
University of Edinburgh
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 158 - 160
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

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