engleski

On a class of module maps of Hilbert C*-modules

The paper describes some basic properties of a class of module maps of Hilbert C*-modules. In Section 1 ideal submodules are considered and the canonical Hilbert C*-module structure on the quotient of a Hilbert C*-module over an ideal submodule is described. Given a Hilbert C*-module V, an ideal submodule , and the quotient , canonical morphisms of the corresponding C*-algebras of adjointable operators are discussed. In the second part of the paper a class of module maps of Hilbert C*-modules is introduced.Given Hilbert C*-modules V and W and a morphism of the underlying \cez-algebras, a map belongs to the class under consideration if it preserves inner products modulo : for all . It is shown that each morphism Φ of this kind is necessarily a contraction such that the kernel of Φ is an ideal submodule of V. A related class of morphisms of the corresponding linking algebras is also discussed.

Hilbert C*-module

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