Work

The class $$C_{0}$$ and the closability property

Year: 2025

Type: article

Abstract: A (not necessarily closed) algebra of operators $$\mathcal{A}$$ A on a Hilbert space is said to have the closability property if every densely defined linear transformation that commutes with $$\mathcal{A}$$ A is closable. We show that an algebra of the form $$\{u(T):u\in H^{\infty}\}$$ { u ( T ) : u ∈ H ∞ } , where T is an operator of class $$C_{0}$$ C 0 , has the closability property precisely when T has a certain finiteness property, usually know as property (P). An analogous result is proved for commutative von Neumann algebras.

Source: Analysis Mathematica

DOI: 10.1007/s10476-025-00119-z

Authors: H. Bercovici, H.-W. Huang

Institutions: Indiana University Bloomington, Indiana University, National Tsing Hua University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W4415730904