Opuscula Mathematica (Jan 2009)

Matrices defined by frames

  • Zbigniew Ambroziński,
  • Krzysztof Rudol

DOI
https://doi.org/10.7494/OpMath.2009.29.4.365
Journal volume & issue
Vol. 29, no. 4
pp. 365 – 375

Abstract

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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