Conditionally positive definite unilateral weighted shifts

초록

In a recent paper [15], Hilbert space operators T with the property that each sequence of the form {IITnhII2}infinity n=0 is con-ditionally positive definite in a semigroup sense were intro-duced. In the present paper, this line of research is continued in depth in the case of unilateral weighted shifts. The condi-tional positive definiteness of unilateral weighted shifts is char-acterized in terms of formal moment sequences. The descrip-tion of the representing triplet, the main object canonically associated with such operators, is provided. The backward ex-tension problem for conditionally positive definite unilateral weighted shifts is solved, revealing a new feature that does not appear in the case of other operator classes. Finally, the flatness problem in this context is discussed with emphases on unexpected differences from the analogous problem for sub-normal unilateral weighted shifts. (c) 2023 Elsevier Inc. All rights reserved.

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