Affiliation:
1. Department of Mathematics-Faculty of Science P.O.Box()- Mu’tah university- Al-Karak, Jordan
Abstract
Let A and B be positive operators and 0 < q ? 1. In this paper, we shall
show that if Aq?0 ? (A?0/2B?0A?0/2) q?0/?0+?0 and (B?0/2A?0B?0/2) q?0/?0+?0
? Bq?0 hold for fixed ?0 > 0 and ?0 > 0. Then the following inequalities
hold: Aq1? ? (A?/2B?A?/2) q1?/?+? and (B?/2A?B?/2) q1?/?+? ? Bq1? for all ?
? ?0, ? ? ?0 and 0 < q1 ? q. Also, we shall show a normality of class p-A(s,
t) for s > 0, t > 0 and 0 < p ? 1. Moreover, we shall show that if T or T*
belongs to class p-wA(s, t) for some s > 0, t > 0 and 0 < p ? 1 and S is an
operator for which 0 ? W(S) and ST = T*S, then T is self-adjoint.
Publisher
National Library of Serbia
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