Connecting $H^{\infty }$-functional calculus and isometric dilations for commuting families of Ritt${}_E$ operators

Christian Le Merdy, M. N. Reshmi

Let $(T_1,\dots ,T_d)$ be a commuting $d$-tuple of Ritt${}_E$ operators on some UMD Banach space $X$. We show that $(T_1,\dots ,T_d)$ admits a bounded $H^{\infty }$-functional calculus…