Opuscula Mathematica (Jan 2009)
Matrices defined by frames
Abstract
Matrix representations of bounded Hilbert space operators are considered. The matrices in question are defined with respect to frames, rather than bases. The frames, a generalisation of bases, used extensively in applied harmonic analysis, are overcomplete sequences. We consider some properties related to tight frames, where, up to some multiplicative constant, a form of Parseval Identity takes place. We also describe parts of spectra of operators in terms of their matrices.
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