Matrix Representation of Operators Using Frames

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dc.creatorBalazs, Peter
dc.date2005-10-07
dc.date2006-11-23
dc.date.accessioned2026-07-07T09:31:08Z
dc.date.available2026-07-07T09:31:08Z
dc.descriptionIn this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is useful to extend the known method of matrix representation by using these sequences instead of ONBs for these application areas. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l2 and operators on the Hilbert space. We will show some structural results and give some examples. Furthermore in the case of Riesz bases we prove that those functions are isomorphisms. Finally we are going to apply this idea to the connection of Hilbert-Schmidt operators and Frobenius matrices. Keywords: frames, discrete expansion, operators, matrix representation, Hilbert-Schmidt operators, Frobenius matrices, Riesz bases.
dc.description16 pages; title was changed; Cut from 25 to 16 pages
dc.identifierhttps://arxiv.org/abs/math/0510146
dc.identifierhttp://arxiv.org/abs/math/0510146
dc.identifierSampling Theory in Signal and Image Processing (STSIP), Vol.7, No. 1, Jan. 2008, pp. 39-54
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158354
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject41A58; 42C15; 47A58; 65J10
dc.titleMatrix Representation of Operators Using Frames
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