ON OPERATOR VALUED WEIGHTED SHIFTS COMMUTING WITH \(U_+\) - Orovčanec, Marija (Matematichki Bilten, 1994)
In this paper we consider some properties of the operators \(K_U_+\) and of the operators on \(K_A\) where \(AK_U_+\). Also we shall give some information about the operators that commutes with \(U_+\). The computations show that operator \(XB(^2(H))\) which commutes with \(U_+\) is the formal power series \[ U_+^*A_0+_i=0^∞U_+^iA_i+1, A_iK_U_+. \] At the end we shall prove that if \((\|A_i\|)_i=0^∞^1\) then the formal power series is a bounded operator and is the limit in uniform operator topology of a sequence of polinomials in \(U_+\).