Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774804 | Journal of Mathematical Analysis and Applications | 2017 | 49 Pages |
Abstract
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is proved that if such an operator is bounded, then its symbol is a polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type model for composition operators with linear symbols is established. As a consequence, explicit formulas for their polar decomposition, Aluthge transform and powers with positive real exponents are provided. The theorem of Carswell, MacCluer and Schuster is generalized to the case of Segal-Bargmann spaces of infinite order. Some related questions are also discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jan Stochel, Jerzy BartÅomiej Stochel,