Invertibility in nest algebras

Avraham Feintuch, Alan Lambert

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let F denote a complete nest of subspaces of a complex Hubert space ℌ, and let C denote the nest algebra defined by F. Let K denote the ideal of compact operators on ℌ. If F has no infinite-dimensional gaps then T ∈ C is invertible in C if and only if it is invertible in C + K. An example is given of a nest with an infinite gap for which there exists an operator in C which is invertible in C + K but not in C.

Original languageEnglish
Pages (from-to)573-576
Number of pages4
JournalProceedings of the American Mathematical Society
Volume91
Issue number4
DOIs
StatePublished - 1 Jan 1984

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