Isometries of real Hilbert C-modules

Ming-Hsiu Hsu Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43735

Journal of Mathematical Analysis and Applications, 438, (2), 807-827, 2016.6
Abstract Let T: V W be a surjective real linear isometry between full real Hilbert C-modules over real C-algebras A and B, respectively. We show that the following conditions are equivalent:(a) T is a 2-isometry;(b) T is a complete isometry;(c) T preserves ternary products;(d) T preserves inner products;(e) T is a module map. When A and B are commutative, we give a full description of the structure of T.
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  title={Isometries of real Hilbert C-modules},
  author={Ming-Hsiu Hsu, and Ngai-Ching Wong},
  booktitle={Journal of Mathematical Analysis and Applications},
Ming-Hsiu Hsu, and Ngai-Ching Wong. Isometries of real Hilbert C-modules. 2016. Vol. 438. In Journal of Mathematical Analysis and Applications. pp.807-827.
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