[PDF] On the Bounds of Symplectic Spectrum-论文阅读讨论-ReadPaper

摘要

In 2018, B. V. Rajarama Bhat and T. C. John developed the Williamson's Normalform for strictly positive invertible operators on infinite-dimensionalseparable real Hilbert spaces and defined symplectic spectrum for theseoperators. Recently an interlacing relation between the eigenvalues andsymplectic eigenvalues for operators with countable spectrum was formulated. Weconsider two different classes of operators and determine the bounds for thesymplectic spectrum using the bounds of the spectrum for some special class ofoperators. We also compute their symplectic spectrum and Williamson's Normalform. In the course, we define the symplectic equivalence of two operators andshow that symplectically equivalent operators will have the same symplecticspectrum. Finally, we illustrate an example of the truncation method using thealgorithm we developed.

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