Conditionally positive definite unilateral weighted shifts

In a recent paper [15], Hilbert space operators T with the property that each sequence of form {‖Tnh‖2}n=0∞ is conditionally positive definite in semigroup sense were introduced. present paper, this line research continued depth case unilateral weighted shifts. The conditional definiteness shifts characterized terms formal moment sequences. description representing triplet, main object canonically associated such operators, provided. backward extension problem for solved, revealing new feature does not appear other operator classes. Finally, flatness context discussed emphases on unexpected differences from analogous subnormal