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- Title
Matrix Representation of Operators Using Frames.
- Authors
Balazs, Peter
- Abstract
This paper addresses how to find a matrix representation of operators on a Hilbert space H 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 H. 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 apply this idea to the connection of Hilbert-Schmidt operators and Frobenius matrices.
- Subjects
OPERATOR theory; MATRICES (Mathematics); FRAMES (Vector analysis); HILBERT space; RIESZ spaces
- Publication
Sampling Theory in Signal & Image Processing, 2008, Vol 7, Issue 1, p39
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/bf03549484