Work

Noncommutative commutant lifting, interpolation, and shift-invariant subspaces

Year: 2026

Type: preprint

Abstract: We establish a Sarason-type commutant lifting theorem in the framework of noncommutative Drury-Arveson space and apply it to solve the noncommutative Nevanlinna-Pick interpolation problem on the noncommutative row ball. In particular, it recovers the classical Nevanlinna-Pick interpolation theorem over the open unit disc. We also provide a Beurling-Lax-Halmos-type characterization of shift-invariant subspaces of noncommutative Drury-Arveson space using dilation theoretic technique.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11410

Authors: Barik, Sibaprasad, Panja, Samir

Institutions: Indian Statistical Institute, Bangalore Centre, Indian Statistical Institute

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, National Board for Higher Mathematics

OpenAlex ID: W7212265461

Cites: 1

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Related to: 10