Unconditional Basis Uniformly Gateaux Smooth Norms Uniform Eberlein Compacts Uniform Rotundity In Every Direction
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 26, No 4, (2000), 353p-358p
It is shown that a Banach space X admits an equivalent uniformly
Gateaux differentiable norm if it has an unconditional basis and X*
admits an equivalent norm which is uniformly rotund in every direction.
*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part
of the author’s MSc thesis written under the supervison of Professor V. Zizler.