PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Truncation and Duality Results for Hopf Image Algebras

Volume 62 / 2014

Teodor Banica Bulletin Polish Acad. Sci. Math. 62 (2014), 161-179 MSC: Primary 46L65; Secondary 46L37. DOI: 10.4064/ba62-2-5


Associated to an Hadamard matrix $H\in M_N(\mathbb C)$ is the spectral measure $\mu\in\mathcal P[0,N]$ of the corresponding Hopf image algebra, $A=C(G)$ with $G\subset S_N^+$. We study a certain family of discrete measures $\mu^r\in\mathcal P[0,N]$, coming from the idempotent state theory of $G$, which converge in Cesàro limit to $\mu$. Our main result is a duality formula of type $\int_0^N(x/N)^p\,d\mu^r(x)=\int_0^N(x/N)^r\,d\nu^p(x)$, where $\mu^r,\nu^r$ are the truncations of the spectral measures $\mu,\nu$ associated to $H,H^t$. We also prove, using these truncations $\mu^r,\nu^r$, that for any deformed Fourier matrix $H=F_M\otimes_QF_N$ we have $\mu=\nu$.


  • Teodor BanicaDepartment of Mathematics
    Cergy-Pontoise University
    95000 Cergy-Pontoise, France

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image