Document Zbl 0573.47016

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Hyponormal operators are subscalar. (English) Zbl 0573.47016

J. Oper. Theory 12, 385-395 (1984).

The paper is centered around a natural scalar extension of a hyponormal operator. In particular it is proved that every hyponormal operator is the restriction to a closed invariant subspace of a generalized scalar operator of order 2. The method of producing the natural scalar extension is constructive and elementary.
See also the paper ”Extensions scalaires et noyaux distribution des opérateurs hyponormaux”, C. R. Acad. Sci., Paris Sér. I 301, 739-741 (1985).

Cited in 6 Reviews

Cited in 65 Documents

MSC:

47B20	Subnormal operators, hyponormal operators, etc.
47B40	Spectral operators, decomposable operators, well-bounded operators, etc.
47A45	Canonical models for contractions and nonselfadjoint linear operators

Keywords:

scalar extension of a hyponormal operator; invariant subspace; generalized scalar operator

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