Truncation and Duality Results for Hopf Image Algebras

Teodor Banica

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014), p. 161-179 / Harvested from The Polish Digital Mathematics Library

Résumé

Associated to an Hadamard matrix $H ∈ M_N(ℂ)$ is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with $G ⊂ S⁺_N$. We study a certain family of discrete measures $μ^r ∈ [0,N]$, coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type $∫_0^N (x/N)^p dμ^r(x) = ∫_0^N (x/N)^r dν^p(x)$, where $μ^r,ν^r$ are the truncations of the spectral measures μ,ν associated to $H,H^t$. We also prove, using these truncations $μ^r,ν^r$, that for any deformed Fourier matrix $H=F_M ⊗_Q F_N$ we have μ = ν.

Détail

Publié le : 2014-01-01

Zbl 1316.46051

EUDML-ID : urn:eudml:doc:281262