Open Access
Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
(European Mathematical Society, 2019) Albiac Alesanco, Fernando José; Ansorena, José L.; Ciaurri, Óscar; Varona, Juan L.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we show that no normalized unconditional basis in L-p, p not equal 2, can be semi-normalized in L-q for q not equal p, thus extending a classical theorem of Kadets and Pelczynski from 1968.
Open Access
Projections and unconditional bases in direct sums of ℓp SPACES, 0
(Wiley, 2021) Albiac Alesanco, Fernando José; Ansorena, José L.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
We show that every unconditional basis in a finite direct sum ⊕p∈Aℓp , with A ⊂ (0,∞], splits into unconditional bases of each summand. This settles a 40 years old question raised in 'A. Ortyński, Unconditional bases in ℓp ⊕ ℓq, 0< p < q <1, Math. Nachr. 103 (1981), 109–116'. As an application we obtain that for any A ⊂ (0,1] finite, the spaces Z = ⊕p∈A ℓp,Z ⊕ ℓ2, and Z ⊕ c0 have a unique unconditional basis up to permutation.

Albiac Alesanco, Fernando José

Email Address