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Mathematics > Functional Analysis

arXiv:1812.08143 (math)
[Submitted on 19 Dec 2018 (v1), last revised 20 May 2019 (this version, v2)]

Title:Hypercontractions and factorizations of multipliers in one and several variables

Authors:Monojit Bhattacharjee, B. Krishna Das, Jaydeb Sarkar
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Abstract:We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foias characteristic functions of contractions. We present an explicit method to compute characteristic functions of hypercontractions and relate characteristic functions by means of the factors of Schur-Agler class of functions and universal multipliers on the unit ball in $\mathbb{C}^n$. We also offer some factorization properties of multipliers. Characteristic functions of hypercontrctions are complete unitary invariant. The Drury-Arveson space and the weighted Bergman spaces on the unit ball continues to play a significant role in our consideration. Our results are new even in the special case of single hypercontractions.
Comments: 31 pages, revised and expanded version
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV); Operator Algebras (math.OA)
MSC classes: 47A13, 47A20, 47A45, 47A48, 47A56, 46E22, 47B32, 32A35, 32A36, 32A70
Cite as: arXiv:1812.08143 [math.FA]
  (or arXiv:1812.08143v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1812.08143

Submission history

From: Jaydeb Sarkar [view email]
[v1] Wed, 19 Dec 2018 18:38:53 UTC (14 KB)
[v2] Mon, 20 May 2019 20:23:51 UTC (22 KB)
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