Optimality of the rearrangement inequality with applications to Lorentz-type sequence spaces
- Resource Type
- Working Paper
- Authors
- Albiac, Fernando; Ansorena, Jose L.; Leung, Denny; Wallis, Ben
- Source
- Subject
- Mathematics - Functional Analysis
26D15 (Primary), 46B15, 46B230, 46B25, 46B45 (Secondary)
- Language
We characterize the sequences $(w_i)_{i=1}^\infty$ of non-negative numbers for which \[ \sum_{i=1}^\infty a_i w_i \quad \text{ is of the same order as } \quad \sup_n \sum_{i=1}^n a_i w_{1+n-i} \] when $(a_i)_{i=1}^\infty$ runs over all non-increasing sequences of non-negative numbers. As a by-product of our work we settle a problem raised in [F. Albiac, Jose L. Ansorena and B. Wallis; arXiv:1703.07772[math.FA]] and prove that Garling sequences spaces have no symmetric basis.