The Agler-Young Class
Functional Analysis
2018-09-25 v3
Abstract
This note introduces a special class of tuples of bounded operators on a Hilbert space. It is called the Agler Young class. Major results about this class include a Wold decomposition and a dilation theorem. The structure of the dilation is completely spelt out. A characterization of this class using the hereditary functional calculus of Agler is obtained and examples are discussed. Toeplitz operators play a major role in this note. An Agler-Young pair arising from a truncated Toeplitz operator is characterized. Thus, we extend results obtained in the case of commuting operators by several authors over many decades to the non-commutative situation. The results for the commuting case can be recovered as special cases.
Cite
@article{arxiv.1712.00940,
title = {The Agler-Young Class},
author = {Tirthankar Bhattacharyya and Subrata Shyam Roy and Tapesh Yadav},
journal= {arXiv preprint arXiv:1712.00940},
year = {2018}
}
Comments
A co-author added