27th Conference of the International Linear Algebra Society (ILAS 2026)

Results on the symplectic spectrum of compact operators

May 21, 2026, 2:25 PM

25m

McBryde Hall 113

Minisymposium Talk Symplectic Linear Algebra and Applications Symplectic Linear Algebra and Applications

Speaker

Anmary Tonny (Indian Institute of Technology, Madras)

Description

In 1936, J. Williamson introduced the Williamson’s normal form for 2n × 2n positive definite real matrices. It is the symplectic analogue of the spectral theorem for normal matrices. In 2019, B. V. R. Bhat and T. C. John proved the infinite-dimensional analogue of the Williamson’s normal form and in 2024, H. K. Mishra extended the Williamson’s normal form to 2n × 2n real symmetric matrices. In this presentation, we extend the Williamson’s normal form to symmetric operators on infinite-dimensional real separable Hilbert spaces and give some results on the symplectic spectrum of compact symmetric operators in light of the generalized Williamson's normal form.