engleski

Synthesis operators of frames in Hilbert C*-modules

Let (x_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 Damir Bakić.

synthesis operator ; frames ; C*-algebra ; Hilbert C*-module

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