# Operator positivity and analytic models of commuting tuples of operators

Monojit Bhattacharjee; Jaydeb Sarkar

Studia Mathematica (2016)

- Volume: 232, Issue: 2, page 155-171
- ISSN: 0039-3223

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topMonojit 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 -

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