Spaces of Bessel generators and characterizations of Bessel generator multipliers for unitary systems (Q522983)

Motivated by the work of \textit{D. Han} and \textit{D. R. Larson} [in: Wavelets and multiscale analysis. Theory and applications. Selected papers based on the presentations at the international conference on wavelets: twenty years of wavelets, DePaul University, Chicago, IL, USA, May 15--17, 2009. New York, NY: Springer. 131--150 (2011; Zbl 1278.42043)], the author in this paper introduces a special subset of frame generators for a unitary system of vector space structure. An isometric isomorphism map from the normed Bessel generator vector space is studied and it is shown that this map is a homomorphism from the vector space of subsets of frame generators to the normed local commutant vector space. Finally, some types of frame generators are characterized. Also, two norms on Bessel multipliers for some cases are compared.