Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions

We consider weighted shift operators having the property of moment infinite divisibility; that is, for any \(p > 0\), is subnormal when every weight (equivalently, moment) raised to p-th power. By reconsidering sequence conditions weights or moments shift, we obtain a new characterization such shifts, and prove shifts are, under mild conditions, robust variety operations also rigid in certain senses. In particular, whose has limit infinitely divisible if only its Aluthge transform is. As consequence, maps class bijectively onto itself. back-step extensions, subshifts, completions.