"Real normal operators and Williamson’s normal form" by B. V. Rajarama Bhat and Tiju Cherian John
 

Real normal operators and Williamson’s normal form

Article Type

Research Article

Publication Title

Acta Scientiarum Mathematicarum

Abstract

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose (adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite-dimensional situation, is also proved using elementary techniques. The second result is used to establish the main theorem of this article, which is a generalization of Williamson’s normal form for bounded positive operators on infinite-dimensional separable Hilbert spaces. This has applications in the study of infinite mode Gaussian states.

First Page

507

Last Page

518

DOI

10.14232/actasm-018-570-5

Publication Date

1-1-2019

Comments

Open Access, Green

This document is currently not available here.

Share

COinS