Vol. 22, No. 3, 1967

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ISSN: 0030-8730
On some hyponormal operators

V. Istrăţescu

Vol. 22 (1967), No. 3, 413–417
Abstract

Let H be a Hilbert space and T a hyponormal operator (TT TT0). The first result is: if (T)pTq is a completely continuous operator then T is normal.

Secondly, part we introduce the class of operators on a Banach space which satisfy the condition

∥x∥ = 1 ∥T x∥2 ≦ ∥T2x∥

and we prove the following:

1. γT = limTn1∕n = T;

2. if T is defined on Hilbert space and is completely continuous then T is normal.

Mathematical Subject Classification
Primary: 47.10
Milestones
Received: 22 December 1965
Published: 1 September 1967
Authors
V. Istrăţescu