Let A and B be real or complex C*-algebras. Let V and W be real or complex (right) full
Hilbert C*-modules over A and B, respectively. Let T be a linear bijective map from V onto
W. We show the following four statements are equivalent.
(a) T is a unitary operator, i.e., there is a ∗-isomorphism £\ : A ¡÷ B such that
<Tx,Ty> = £\(<x,y>), ∀ x,y∈ V ;
(b) T preserves TRO products, i.e., T(x<y,z>) =Tx<Ty,Tz>, ∀ x,y,z in V ;
(c) T is a 2-isometry;
(d) T is a complete isometry.
Moreover, if A and B are commutative, the four statements are also equivalent to
(e) T is a isometry.
On the other hand, if V and W are complex Hilbert C*-modules over complex C*-algebras,
then T is unitary if and only if it is a module map, i.e.,
T(xa) = (Tx)£\(a), ∀ x ∈ V,a ∈ A.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0723112-130530 |
| Date | 23 July 2012 |
| Creators | Hsu, Ming-Hsiu |
| Contributors | Man-Duen Choi, Mau-Hsiang Shih, Hwa-Long Gau, Mao-Ting Chien, Pei-Yuan Wu, Ngai-Ching Wong, Chi-Kwong Li |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0723112-130530 |
| Rights | user_define, Copyright information available at source archive |
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