Opuscula Math. 29, no. 4 (2009), 365-375
http://dx.doi.org/10.7494/OpMath.2009.29.4.365
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.
- Zbigniew Ambroziński
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
- Krzysztof Rudol
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
- Received: 2009-06-24..
- Revised: 2009-08-13.
- Accepted: 2009-08-20.
