ACTA issues

Basic properties of the generalized Kantorovich constant $K{(h,p)}={(h^p-h)\over(p-1)(h-1)}\left({(p-1)\over p}{(h^p-1)\over(h^p-h)}\right )^p$ and its applications

Takayuki Furuta

Acta Sci. Math. (Szeged) 70:1-2(2004), 319-337

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.)