Operator positivity and analytic models of commuting tuples of operators

Monojit Bhattacharjee, and Jaydeb Sarkar. "Operator positivity and analytic models of commuting tuples of operators." Studia Mathematica 232.2 (2016): 155-171. <http://eudml.org/doc/286181>.

@article{MonojitBhattacharjee2016,
abstract = {We study analytic models of operators of class $C_\{·0\}$ with natural positivity assumptions. In particular, we prove that for an m-hypercontraction $T ∈ C_\{·0\}$ on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that $ ≅ _\{θ\} = A²ₘ(⁎) ⊖ θH²()$ and $T ≅ P_\{_\{θ\}\} M_\{z\}|_\{_\{θ\}\}$, 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.},
author = {Monojit Bhattacharjee, Jaydeb Sarkar},
journal = {Studia Mathematica},
keywords = {weighted Bergman spaces; hypercontractions; multipliers; reproducing kernel Hilbert spaces; invariant subspaces},
language = {eng},
number = {2},
pages = {155-171},
title = {Operator positivity and analytic models of commuting tuples of operators},
url = {http://eudml.org/doc/286181},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Monojit Bhattacharjee
AU - Jaydeb Sarkar
TI - Operator positivity and analytic models of commuting tuples of operators
JO - Studia Mathematica
PY - 2016
VL - 232
IS - 2
SP - 155
EP - 171
AB - We study analytic models of operators of class $C_{·0}$ with natural positivity assumptions. In particular, we prove that for an m-hypercontraction $T ∈ C_{·0}$ on a Hilbert space , there exist Hilbert spaces and ⁎ and a partially isometric multiplier θ ∈ ℳ (H²(),A²ₘ(⁎)) such that $ ≅ _{θ} = A²ₘ(⁎) ⊖ θH²()$ and $T ≅ P_{_{θ}} M_{z}|_{_{θ}}$, 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.
LA - eng
KW - weighted Bergman spaces; hypercontractions; multipliers; reproducing kernel Hilbert spaces; invariant subspaces
UR - http://eudml.org/doc/286181
ER -