Weak null maximum and integration of families of multiplication operators
Abstract
Let X X be a reflexive Hardy space or weighted Bergman space on the unit disk in the complex plane. For a bounded linear operator S S on X X , let w e m ( S ) ≔ sup ( f n ) lim sup n ‖ S f n ‖ wem(S)≔\sup _{(f_n)} \limsup _n \|Sf_n\| , that is, the supremum of cluster points of n ↦ ‖ S f n ‖ n\mapsto \|S f_n\| , where ( f n ) (f_n) is any unit norm weakly null sequence. This quantity coincides with the essential norm on the reflexive weighted Bergman spaces. For a suitable family { g t : t ∈ ] 0 , 1 [ } \{ g_t : t\in ]0,1[ \} of bounded analytic functions on the unit disk, we characterize when one can exchange w e m ( ⋅ ) wem(\cdot ) and integration over t t of the multiplication operators M
Fields of Study & Subjects
Approximation Theory and Sequence Spaces
Holomorphic and Operator Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4361–4369
- Publication date
- 13 May 2026
- Language
- EN