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A Hilbert C*-module over a C*-algebra A is a right A-module X equipped with an A-valued inner product such that X is a Banach space with respect to the norm induced from A. We discuss frames in X. In this talk we present some new results in the theory of frames for countably generated Hilbert C*-modules over arbitrary C*- algebras. In investigating the nonunital case we introduce the concept of an outer frame for X - in comparison with frames for X the difference is that the elements of an outer frame for X are merely members of a multiplier module M(X) and need not belong to X. Outer frames behave very much like frames ; for example, the reconstruction property for elements of X is preserved, and the only adjointable operators on M(X) that preserve the class of frames and outer frames for X are the surjective ones. Building on a unified approach to frames and outer frames we obtain new results on dual frames, frame perturbations, tight approximations of frames and finite extensions of Bessel sequences. This is a joint work with Damir Bakić.
Hilbert C*-module ; C*-algebra ; outer frames ; modular frame
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