Inner Products and Module Maps of Hilbert C∗-modules

نویسنده

  • MING-HSIU HSU
چکیده

Let E and F be two Hilbert C∗-modules over C∗-algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and φ a map from A into B. We will prove in this paper that if the C∗-algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a ∗-isomorphism φ between the C∗-algebras such that 〈Tx, Ty〉 = φ(〈x, y〉), and T (xa) = T (x)φ(a). In case A or B is noncommutative C∗-algebra, T may not satisfy the equations above in general. We will also give some condition such that T preserves the inner products and T is a module map.

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تاریخ انتشار 2012