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

D. Bakić
B. Guljaš


Puni tekst: engleski pdf 200 Kb

str. 177-192

preuzimanja: 1.972

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Sažetak

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 V\inss, and the quotient V/V\inss, 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 φ:\ass\bss of the underlying \cez-algebras, a map Φ:VW belongs to the class under consideration if it preserves inner products modulo φ: Φ(x),Φ(y)=φ(x,y) for all x,yV.
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.

Ključne riječi

C*-algebra; Hilbert C*-module; adjointable operator

Hrčak ID:

775

URI

https://hrcak.srce.hr/775

Datum izdavanja:

17.12.2002.

Posjeta: 2.836 *

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