Journal article
Symmetric Pairs of Unbounded Operators in Hilbert Space, and Their Applications in Mathematical Physics
Mathematical physics, analysis, and geometry, Vol.20(2), pp.1-24
04/01/2017
DOI: 10.1007/s11040-017-9245-1
Abstract
In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair consists of two densely defined linear operators
A
and
B
, with
A
⊆
B
⋆
and
B
⊆
A
⋆
. In this paper, we will show by example that symmetric pairs may be used to deduce closability of operators and sometimes even compute adjoints. In particular, we prove that the Malliavin derivative and Skorokhod integral of stochastic calculus are closable, and the closures are mutually adjoint. We also prove that the basic involutions of Tomita-Takesaki theory are closable and that their closures are mutually adjoint. Applications to functions of finite energy on infinite graphs are also discussed, wherein the Laplace operator and inclusion operator form a symmetric pair.
Details
- Title: Subtitle
- Symmetric Pairs of Unbounded Operators in Hilbert Space, and Their Applications in Mathematical Physics
- Creators
- Palle E. T Jorgensen - University of IowaErin P. J Pearse - California Polytechnic State University
- Resource Type
- Journal article
- Publication Details
- Mathematical physics, analysis, and geometry, Vol.20(2), pp.1-24
- DOI
- 10.1007/s11040-017-9245-1
- ISSN
- 1385-0172
- eISSN
- 1572-9656
- Publisher
- Springer Netherlands
- Language
- English
- Date published
- 04/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240872102771
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