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Wavelet representations and Fock space on positive matrices
Journal article   Open access   Peer reviewed

Wavelet representations and Fock space on positive matrices

P.E.T Jorgensen and D.W Kribs
Journal of functional analysis, Vol.197(2), pp.526-559
2003
DOI: 10.1016/S0022-1236(02)00026-5
url
https://doi.org/10.1016/S0022-1236(02)00026-5View
Published (Version of record) Open Access

Abstract

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz–Toeplitz isometries as a special case.
Hilbert space Creation operators Fock space Completely positive map Cuntz algebra Biorthogonal wavelet

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