(1) Indian Statistical Institute, R.V. College Post, 560 059 Bangalore, India
Abstract:
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when
the space of compact operators is anM-ideal in the space of bounded operators, a very smooth operatorT attains its norm at a unique vectorx (up to a constant multiple) andT(x) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball
has a very smooth point then the space has the Radon-Nikodym property. We give an example of a smooth Banach space without
any very smooth points.