Work

An application of generalised limits to obtain continuous- from discrete time dilations

Year: 2025

Type: article

Abstract: Ptak (Ann. Polon. Math. 45 (3), 237–243 (1985)) introduced an elegant method in the separable setting that allows us to deduce dilation results for continuous semigroups of contractions from the corresponding discrete versions. The purpose of this note is to record another such trick using generalised limits that shows that dilation results for semigroups of contractions in continuous time come for free once we establish them in discrete time. Moreover, it works for non-separable Hilbert spaces and bypasses the theory of unbounded operators.

Source: Semigroup Forum

DOI: 10.1007/s00233-025-10507-4

Author: S. Sundar

Institutions: Homi Bhabha National Institute, Institute of Mathematical Sciences

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Institute of Mathematical Sciences