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.
Originalsprache | englisch |
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Titel | Non-Selfadjoint Operators in Quantum Physics |
Untertitel | Mathematical Aspects |
Herausgeber (Verlag) | Wiley |
Kapitel | 5 |
Seiten | 241-291 |
Seitenumfang | 51 |
ISBN (elektronisch) | 9781118855300 |
ISBN (Print) | 9781118855287 |
DOIs | |
Publikationsstatus | Veröffentlicht - 31 Juli 2015 |
Extern publiziert | Ja |
ASJC Scopus subject areas
- Physik und Astronomie (insg.)
- Ingenieurwesen (insg.)
- Mathematik (insg.)