Essential norms of weighted composition operators from reproducing kernel Hilbert spaces into weighted-type spaces. (English) Zbl 1360.47004
Summary: In this work, we study weighted composition operators acting on a reproducing kernel Hilbert space of analytic functions and mapping into a weighted-type Banach space or a Bloch-type space. Our main result is an approximation of the essential norm of such operators. Moreover, we obtain an exact formula for the operator norm and the essential norm when the operator maps certain weighted Hardy spaces, including the Hardy Hilbert space, the Bergman Hilbert space, and the logarithmic Bergman Hilbert space into a weighted-type Banach space.
MSC:
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
| 47B33 | Linear composition operators |
| 30H05 | Spaces of bounded analytic functions of one complex variable |
| 46E22 | Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) |
