Izvorni znanstveni članak
On a class of module maps of Hilbert C*-modules
D. Bakić
B. Guljaš
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 $\varphi : \ass \rightarrow \bss$ of the underlying \cez-algebras, a map $\Phi : V \rightarrow W$ belongs to the class under consideration if it preserves inner products modulo $\varphi$: $\langle \Phi(x), \Phi(y) \rangle = \varphi(\langle x,y \rangle)$ for all $x,y \in V$.
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
Datum izdavanja:
17.12.2002.
Posjeta: 2.753 *