We study analytic models of operators of class with natural positivity assumptions. In particular, we prove that for an m-hypercontraction on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that and , where A²ₘ(⁎) is the ⁎-valued weighted Bergman space and H²() is the -valued Hardy space over the unit disc . We then proceed to study analytic models for doubly commuting n-tuples of operators and investigate their applications to joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over the polydisc. In particular, we completely analyze doubly commuting quotient modules of a large class of reproducing kernel Hilbert modules, in the sense of Arazy and Engliš, over the unit polydisc ⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8437-2-2016,
author = {Monojit Bhattacharjee and Jaydeb Sarkar},
title = {Operator positivity and analytic models of commuting tuples of operators},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {155-171},
zbl = {06575028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8437-2-2016}
}
Monojit Bhattacharjee; Jaydeb Sarkar. Operator positivity and analytic models of commuting tuples of operators. Studia Mathematica, Tome 233 (2016) pp. 155-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8437-2-2016/