Left multipliers of reproducing kernel Hilbert $C^*$-modules and the Papadakis theorem
| Autor: | Ghaemi, M., Manuilov, V. M., Moslehian, M. S. |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J. Math. Anal. Appl. 505 (2022), no. 1, 125471 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2021.125471 |
| Popis: | We give a modified definition of a reproducing kernel Hilbert $C^*$-module (shortly, $RKHC^*M$) without using the condition of self-duality and discuss some related aspects; in particular, an interpolation theorem is presented. We investigate the exterior tensor product of $RKHC^*M$s and find their reproducing kernel. In addition, we deal with left multipliers of $RKHC^*M$s. Under some mild conditions, it is shown that one can make a new $RKHC^*M$ via a left multiplier. Moreover, we introduce the Berezin transform of an operator in the context of $RKHC^*M$s and construct a unital subalgebra of the unital $C^*$-algebra consisting of adjointable maps on an $RKHC^*M$ and show that it is closed with respect to a certain topology. Finally, the Papadakis theorem is extended to the setting of $RKHC^*M$, and in order for the multiplication of two specific functions to be in the Papadakis $RKHC^*M$, some conditions are explored. Comment: 15 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|