Abstract:

The paper introduces the definitions of continuous operator-valued frame disjointness, strong disjointness strong complement and discusses their properties in Hilbert spaces. Then disjointness-preseving operators, strong disjointness-preseving operators are introduced. It proves that unitary operators,invertible operators are strong disjointness-preseving operators and lower bounded operators, isometric operators are disjointness-preseving operators.

Key words: continuous operator-valued frames; disjointness; disjointness-preseving operator