1. Isometries of real Hilbert C⁎-modules.
- Author
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Hsu, Ming-Hsiu and Wong, Ngai-Ching
- Subjects
- *
HILBERT modules , *MATHEMATICAL equivalence , *TERNARY system , *COMMUTATIVE algebra , *APPLIED mathematics , *MATHEMATICAL analysis - 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 . [ABSTRACT FROM AUTHOR]
- Published
- 2016
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