A Szegő type theorem and distribution of symplectic eigenvalues
Rajendra Bhatia
Ashoka University, Sonepat, IndiaTanvi Jain
Indian Statistical Institute, New Delhi, IndiaRitabrata Sengupta
Indian Institute of Science, Education, & Research (IISER), Berhampur, India
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Abstract
We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szegő 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.
Cite this article
Rajendra Bhatia, Tanvi Jain, Ritabrata Sengupta, A Szegő type theorem and distribution of symplectic eigenvalues. J. Spectr. Theory 11 (2021), no. 3, pp. 1369–1389
DOI 10.4171/JST/377