Glasnik Matematicki, Vol. 41, No.2 (2006), 317-328.

FRAMES OF SUBMODULES FOR COUNTABLY GENERATED HILBERT K(H)-MODULES

Ljiljana Arambašić

Abstract.   In this paper we introduce frames of submodules for countably generated Hilbert K(H)-modules. We show the correspondence between frames of submodules for a Hilbert K(H)-module V and frames of subspaces for the Hilbert space Ve ⊂ V, where e ∈ K(H) is an arbitrary orthogonal one-dimensional projection. We also establish a relation between their frame operators.

2000 Mathematics Subject Classification.   46H25, 46L05, 46L99.

Key words and phrases.   C*-algebra, Hilbert C*-module, compact operator, frame, frame operator, frame of subspaces, frame of submodules.

DOI: 10.3336/gm.41.2.14

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