José L. Ansorena

Banach spaces with a unique greedy basis

The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c 0 , ź 1 , and ź 2 ) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected.

Garling sequence spaces

By generalizing a construction of Garling, for each

Bayoumi quasi-differential is not different from Fréchet-differential

1\leqslant p<\infty

1-greedy renormings of Garling sequence spaces

and each normalized, nonincreasing sequence of positive numbers

Characterization of Weighted Besov Spaces

w\in c_0\setminus\ell_1

Characterization of 1 -quasi-greedy bases

we exhibit an

Lorentz Spaces and Embeddings Induced by Almost Greedy Bases in Banach Spaces

\ell_p

Integration in quasi-Banach spaces and the fundamental theorem of calculus☆

-saturated, complementably homogeneous Banach space

Atomic Decomposition of Weighted Besov Spaces

g(w,p)

Isomorphic classification of mixed sequence spaces and of Besov spaces over [0, 1]d

related to the Lorentz sequence space