An Invariant for Certain Operator Algebras

R. W. Carey, J. D. Pincus
1974 Proceedings of the National Academy of Sciences of the United States of America  
It is shown that the so-called principal function invariant, which is associated in a unitarily invariant way to operators with trace class self commutator TT* -T*T, is invariant under trace class perturbations of T and is an extension of the index of T-z to the whole plane. The connection of the principal function, under additional hypothesis, with the determination of the maximal ideal space of the C* algebra generated by T is discussed, and it is shown that the principal function, even when
more » ... t takes noninteger values, plays a role in establishing the existence of invariant subspaces for T and in determining the point spectrum of T. This note continues the investigation of the properties of the so-called principal function of an almost normal operator. When T is a bounded completely non-normal operator on a Hilbert space H with self commutator TT
doi:10.1073/pnas.71.5.1952 pmid:16592156 pmcid:PMC388361 fatcat:trzavpybojfijnal6nuwajfmw4