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Multiplicative mappings of operator algebras. (English) Zbl 1028.47051
Summary: Nest algebras are the natural analogues of upper triangular matrix algebras in an infinite dimensional Hilbert space. In this paper, we study multiplicative isomorphisms of subalgebras of nest algebras which contain all finite rank operators but might contain no idempotents. We prove that such multiplicative mappings are automatically additive and linear (or conjugate linear).

MSC:
47L35Nest algebras, CSL algebras
46H10Ideals and subalgebras of topological algebras
47L20Operator ideals
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References:
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