Extension of isometries in real Hilbert spacesopen access
- Authors
- Jung, Soon-Mo
- Issue Date
- 1-Jan-2022
- Publisher
- DE GRUYTER POLAND SP Z O O
- Keywords
- isometry; extension of isometry; generalized linear span
- Citation
- OPEN MATHEMATICS, v.20, no.1, pp.1353 - 1379
- Journal Title
- OPEN MATHEMATICS
- Volume
- 20
- Number
- 1
- Start Page
- 1353
- End Page
- 1379
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/30563
- DOI
- 10.1515/math-2022-0518
- ISSN
- 2391-5455
- Abstract
- The main purpose of this article is to develop a theory that extends the domain of any local isometry to the whole space containing the domain, where a local isometry is an isometry between two proper subsets. In fact, the main purpose of this article consists of the following three detailed objectives: The first objective is to extend the bounded domain of any local isometry to the first-order generalized linear span. The second one is to extend the bounded domain of any local isometry to the second-order generalized linear span. The third objective of this article is to extend the bounded domain of any local isometry to the whole Hilbert space.
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