New Sequence Spaces and Function Spaces on Interval [0, 1]. (24th September 2013) - Xu, Cheng-Zhong; Xu, Gen-Qi
Abstract : We study the sequence spaces and the spaces of functions defined on interval 0, 1 in this paper. By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces between ℓ p and ℓ q and function spaces that are interpolating into the spaces between the polynomial space P 0, 1 and C ∞ 0, 1 . We prove that these spaces of sequences and functions are Banach spaces.