Wavelet representations and Fock space on positive matrices

2002/04/02 by P. E. T. Jorgensen, P.E.T. Jorgensen, D. W. Kribs +1 · 2 citations
Mathematics · #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.CA #math.OA #msc:42A16 #msc:42A65 #msc:42C40 #msc:43A65

paper · pdf · doi:10.1016/s0022-1236(02)00026-5

published as J. Funct. Anal. 197 (2003), 526-559 · 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Anal

arxiv created 2002/04/02 · openalex publication_date 2003/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Completely positive linear maps on complex matrices
• Subalgebras of C*-algebras

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