2023/01/22 by B. Krishna Das, Das, B. Krishna, Samir Panja +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2301.09153
openalex publication_date 2023/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The article deals with isometric dilation and commutant lifting for a class of n-tuples (n ≥ 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≥ 3) of commuting contractions each of which possesses isometric dilation.