On Schwarz norms

Abstract

Abstract Investigation of the properties of the numerical radius by Berger and Stampfli showed that indeed numerical radius norm is a Schwarz norm. Later on James P.Williams determined a family of distinct Schwarz norms by slightly modifying the Berger-Stampfli argument. In this thesis we have proved that by slight modification of the S; class constructed by Williams ,we can obtain a class SQ of Schwarz norms, for a positive hermitian operator Q where Q = cI(c ;:: l).We have also determined the scope of the new class of Schwarz norms constructed in terms of the underlying space. Finally we have given the characterizations for the Hilbert space given a contraction; T E B(tl) , IITII ::;1