ON THE FRECHET DIFFERENTIABILITY OF LUXEMBURG NORM IN THE SEQUENCE SPACES l^{p_n} WITH VARIABLE EXPONENTS

Abstract

It is shown that the Luxemburg norm in the sequence space l^{(p_n)} with variable exponents is Frechet - differentiable and a formula expressing the Frechet derivative of this norm at any nonzero x ∈ l^{(p_n)} is given.

Keywords

• Banach sequence space
• smooth space
• Fr´echet - differentiability of the norm