Opuscula Math. 29, no. 4 (2009), 365-375
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.
Keywords: frames, operators, spectrum.
Mathematics Subject Classification: 47A05, 47B10, 42C15.