The Journal of the Indian Mathematical Society

Vasile Istratescu ¹

Affiliations
1 Institut de Mathematique Academie de la Republique Socialists de Roumanie, Bucarest, RO

Abstract

The following lemma was proved by O'Raifeartaigh and Segal [2], [1].

Lemma. If T is a normal operator on a Hilbew space and if for some integer n, x is in the domain of Tⁿ and Tⁿx = 0 then Tx = 0.

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Vasile Istratescu ¹

Affiliations
1 Institute of Mathematics, Rumanian Academy, str. Calea Grivitei 21, Bucharest-12, RO

Abstract

An operator T defined on a Hilbert space H is said to be hyponormal if for every x ∈ H, || T* x || < || Tx ||. The numerical range of an operator T is the set W(T) defined by the relation.

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