Journal article
Block-Toeplitz Operators On the Hardy Space Induced by a Tracial Unital Banach ∗-Probability Space: Block-Toeplitz Operators On the Hardy Space
Aequationes mathematicae, Vol.100(3), 45
04/13/2026
DOI: 10.1007/s00010-026-01283-9
Abstract
For a fixed unital Banach ∗-probability space (A, τ ), we construct a definite, or indefinite inner product space (A0, [, ]τ ), where A0 = A/ker (τ ) is the quotient Banach space and [, ]τ is a definite, or indefinite inner product on A0 determined by the trace τ on the unital Banach ∗-algebra A. From this Banach space (A0, [, ]τ ), a functional vector space, called the A0-Hardy space HA0:2 (D1), is constructed, where D1 is the open unit ball of A0. Similar to the classical Toeplitz-operator theory, one can define Toeplitz-like adjointable Banach-space operators acting on HA0:2 (D1). Our main results characterizes operator-theoretic properties of those Toeplitz-like operators over (A, τ ). In particular, self-adjointness, projection-property, normality, isometry-property, and unitarity are characterized as in the usual operator theory on Hilbert spaces. As application, we study free distributions of certain types of our operator-valued Toeplitz-like operators.
Details
- Title: Subtitle
- Block-Toeplitz Operators On the Hardy Space Induced by a Tracial Unital Banach ∗-Probability Space: Block-Toeplitz Operators On the Hardy Space
- Creators
- Ilwoo Cho - University of IowaPalle E. T. Jorgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Aequationes mathematicae, Vol.100(3), 45
- DOI
- 10.1007/s00010-026-01283-9
- ISSN
- 0001-9054
- eISSN
- 1420-8903
- Publisher
- Springer International Publishing
- Language
- English
- Date published
- 04/13/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985153516802771
Metrics
1 Record Views