engleski

Synthesis operators of frames in Hilbert C*-modules

Let (x_n)_n be a frame for a Hilbert A-module X. Its synthesis operator is a surjective adjointable map from \ell^2(A) to X. If A is a unital C*-algebra, then there is a bijective correspondence of the set of all adjointable surjections from \ell^2(A) to X and the set of all frames for X. In the non-unital case this does not hold ; namely, some adjointable surjections from \ell^2(A) to X are not synthesis operators of any frame for X. However, it turns out that such operators produce frame-like sequences that we call outer frames for X. This is a joint work with D. Bakić.

Hilbert C*-modules ; frames ; synthesis operator

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