engleski

Hilbert C*-modules over C*-algebras of compact operators

A concept of an orthonormal basis for Hilbert \cez-modules is discussed. It is proved that each Hilbert \cez-module $W$ over an arbitrary \cez-algebra \as of (not necessarily all) compact operators on a Hilbert space possesses an orthonormal basis. The \cez-algebra of all adjointable operators on $W$ is naturally represented on a Hilbert space contained in $W$. Also, "compact" operators on $W$ are characterized.

C*-algebra ; Hilbert C*-module ; orthonormal basis ; compact operator ; adjointable operator

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