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14 października 2025 / October 14, 2025
Michał Buchała
m-isometric weighted shifts with operator weights: an application to dilations of m-concave operators (cont.)
Abstract. In the talk we are going to present the characterization of m-isometric weighted shifts with operator weights. The question when the weights of such a shift commute will be answered and the solution to the completion problem will be given. The second part of the presentation will be devoted to applying the aforementioned characterization to dilation theory - we are going to show that every expansive m-concave operator has an m-isometric dilation; the obtained dilation will be proved to be minimal. We will also show that in such a setting minimal dilations may not be unitarily isomorphic. The talk is based on:
1. M. Buchała, m-isometric weighted shifts with operator weights, Bull. Malays. Math. Sci. Soc. 48 (2025).
2. M. Buchała, Every expansive m -concave operator has m -isometric dilation, link.