A Szego type theorem and distribution of symplectic eigenvalues

Authors

Rajendra Bhatia, Ashoka University
Tanvi Jain, Indian Statistical Institute (Delhi Centre)
Ritabrata Sengupta, Indian Institute of Science Education and Research Berhampur

Article Type

Research Article

Publication Title

Journal of Spectral Theory

Abstract

We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szego limit theorem for symplectic eigenvalues, derive an expression for the entropy rate of stationary quantum Gaussian processes, and study the distribution of symplectic eigenvalues of truncated block Toeplitz matrices. We also introduce a concept of symplectic numerical range, analogous to that of numerical range, and study some of its basic properties, mainly in the context of block Toeplitz operators.

First Page

1369

Last Page

1389

DOI

10.4171/JST/377

Publication Date

1-1-2021

Comments

Open Access, Gold, Green

Recommended Citation

Bhatia, Rajendra; Jain, Tanvi; and Sengupta, Ritabrata, "A Szego type theorem and distribution of symplectic eigenvalues" (2021). Journal Articles. 2158.
https://digitalcommons.isical.ac.in/journal-articles/2158