"A Solution To A Problem Of J. R. Ringrose" by David R. Larson

Mathematics, Department of

 

Document Type

Article

Date of this Version

1982

Citation

Bulletin (New Series) Of The American Mathematical Society Volume 7, Number 1, July 1982

Comments

© 1982 American Mathematical Society

Abstract

We announce a solution to a multiplicity problem for nests posed by J. R. Ringrose approximately twenty years ago. This also answers a question posed by R. V. Kadison and I. M. Singer, and independently by I. Gohberg and M. Krein concerning the invariant subspace lattice of a compact operator. The key to the proof is a result concerning compact perturbations of nest algebras which was recently obtained by Niels Andersen in his doctoral dissertation. The complete proof of the general result as well as of a number of related results will appear elsewhere. A proof for the special case which answers Ringrose's original question is included herein.

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