Entropy and Multivariable Interpolation is popular PDF and ePub book, written by Gelu Popescu in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Entropy and Multivariable Interpolation can be Read Online from any device for your convenience.
Entropy and Multivariable Interpolation Book PDF Summary
We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive multi-Toeplitz kernels on free semigroups (resp. multi-analytic operators) and consequences concerning the extreme points of the unit ball of the noncommutative analytic Toeplitz algebra $F_n^\infty$.We obtain several geometric characterizations of the central intertwining lifting, a maximal principle, and a permanence principle for the noncommutative commutant lifting theorem. Under certain natural conditions, we find explicit forms for the maximal entropy solution of this multivariable commutant lifting theorem. All these results are used to solve maximal entropy interpolation problems in several variables. We obtain explicit forms for the maximal entropy solution (as well as its entropy) of the Sarason, Caratheodory-Schur, and Nevanlinna-Pick type interpolation problems for the noncommutative (resp. commutative) analytic Toeplitz algebra $F_n^\infty$ (resp. $W_n^\infty$) and their tensor products with $B({\mathcal H}, {\mathcal K})$. In particular, we provide explicit forms for the maximal entropy solutions of several interpolation problems on the unit ball of $\mathbb{C}^n$.
Detail Book of Entropy and Multivariable Interpolation PDF
- Author : Gelu Popescu
- Release : 26 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821839126
- Genre : Mathematics
- Total Page : 83 pages
- Language : English
- PDF File Size : 10,8 Mb
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