On frames for countably generated Hilbert C*-modules

By Ljiljana Arambašić. 2006

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Let V be a countably generated Hilbert C*-module over a C*-algebra A. We prove that a sequence {;f(i) : i is an element of I}; subset of V is a standard frame for V if and only if the sum Sigma(i is an element of I) converges in norm for every x is an element of V and if there are constants C, D > 0 such that C parallel to x parallel to(2) = parallel to Sigma(i is an element of I) parallel to <= D parallel to x parallel to(2) for every x is an element of V. We also prove that surjective adjointable operators preserve standard frames. A class of frames for countably generated Hilbert C*-modules over the C*-algebra of all compact operators on some Hilbert space is discussed.

Subfields: Applied Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/3f62937ddfade2dbd5f21b3c2e64cc043cf6987e