Frames and outer frames for Hilbert C*-modules (CROSBI ID 228963)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Arambašić, Ljiljana ; Bakić, Damir
engleski
Frames and outer frames for Hilbert C*-modules
The goal of the present paper is to extend the theory of frames for countably generated Hilbert C*-modules over arbitrary C*-algebras. In investigating the non-unital case, we introduce the concept of outer frame as a sequence in the multiplier module M(X) that has the standard frame property when applied to elements of the ambient module X. Given a Hilbert A-module X, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalized Hilbert space l^2(A) to X and the set consisting of all both frames and outer frames for X. Building on a unified approach to frames and outer frames, we then obtain new results on dual frames, frame perturbations, tight approximations of frames and finite extensions of Bessel sequences.
Hilbert C*-module ; frame ; outer frame ; strict frame ; multiplier module
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Podaci o izdanju
65 (2)
2017.
381-431
objavljeno
0308-1087
1563-5139
10.1080/03081087.2016.1186588