|
Abstract. In what follows, an operator means a bounded linear operator on a Hilbert space {\it H}. We shall investigate several basic properties of the {\it generalized Kantorovich constant } and its applications to related results. Firstly we shall show that Kantorovich type inequality for $1 > p>0$ and Kantorovich type one for $ p< 0$ are both obtained by Kantorovich type one for $p>1$. Secondly we shall show that these three Kantorovich type inequalities are mutually equivalent.
AMS Subject Classification
(1991): 47A63
Keyword(s):
Generalized Kantorovich constant,
Kantorovich type inequality,
Specht ratio
Received November 14, 2002, and in revised form December 12, 2002. (Registered under 5816/2009.)
|