Elements of spectral theory without the spectral theorem

David Krejčiřík*, Petr Siegl

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in Buch/BerichtBegutachtung

Abstract

This chapter is mainly devoted to a collection of basic facts from the spectral theory of operators in Hilbert spaces. It summarizes some efficient methods how to construct a closed operator with nonempty resolvent set. The chapter also talks about operators that are similar to self-adjoint (or more generally normal) operators. It recalls the notion of pseudospectra as more reliable information about non-self-adjoint operators than the spectrum itself and collects some abstract methods that can be effectively used to construct a quasi-m-accretive operator from a formal expression. Symmetric forms are familiar in quantum mechanics, where they have a physical interpretation of expectation values. For non-self-adjoint operators, a more general class of sectorial forms is needed. The theory of compact operators in Hilbert spaces is reminiscent of the theory of operators in finite-dimensional spaces. Highly non-self-adjoint operators have properties very different from self-adjoint or normal operators.

Originalspracheenglisch
TitelNon-Selfadjoint Operators in Quantum Physics
UntertitelMathematical Aspects
Herausgeber (Verlag)Wiley
Kapitel5
Seiten241-291
Seitenumfang51
ISBN (elektronisch)9781118855300
ISBN (Print)9781118855287
DOIs
PublikationsstatusVeröffentlicht - 31 Juli 2015
Extern publiziertJa

ASJC Scopus subject areas

  • Physik und Astronomie (insg.)
  • Ingenieurwesen (insg.)
  • Mathematik (insg.)

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