Abstract
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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