Opuscula Math. 29, no. 4 (2009), 365-375

Opuscula Mathematica

Matrices defined by frames

Zbigniew Ambroziński
Krzysztof Rudol

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.

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Cite this article as:
Zbigniew Ambroziński, Krzysztof Rudol, Matrices defined by frames, Opuscula Math. 29, no. 4 (2009), 365-375, http://dx.doi.org/10.7494/OpMath.2009.29.4.365

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