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arXiv · 2301.09153

Isometric dilation and Sarason's commutant lifting theorem in several variables

B. Krishna Das·Samir Panja
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Abstract

The article deals with isometric dilation and commutant lifting for a class of $n$-tuples $(n \geq 3)$ of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a consequence of such an explicit dilation, we show that their von Neumann inequality holds on a one dimensional variety of the closed unit polydisc. On the basis of such a dilation, we prove a commutant lifting theorem of Sarason's type by establishing that every commutant can be lifted to the dilation space in a commuting and norm preserving manner. This further leads us to find yet another class of $n$-tuples $(n\geq 3)$ of commuting contractions each of which possesses isometric dilation.

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BibTeXRIS

B. Krishna Das, Samir Panja. 2023-01-22. Isometric dilation and Sarason's commutant lifting theorem in several variables. https://doi.org/10.4153/s0008414x24000749

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