Complex-self-adjointness

M. Cristina Câmara; David Krejcirik

Complex-self-adjointness

Functional Analysis 2023-04-14 v1 Mathematical Physics math.MP Spectral Theory

Authors: M. Cristina Câmara , David Krejcirik

Abstract

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions, and antilinear eigenfunction expansions. The study is motivated by physical symmetries in quantum mechanics with non-self-adjoint operators.

Keywords

operator theory on hilbert spaces operator theory pseudodifferential operators

Cite

@article{arxiv.2208.05739,
  title  = {Complex-self-adjointness},
  author = {M. Cristina Câmara and David Krejcirik},
  journal= {arXiv preprint arXiv:2208.05739},
  year   = {2023}
}