کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590309 1334947 2014 64 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Operator algebras and subproduct systems arising from stochastic matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Operator algebras and subproduct systems arising from stochastic matrices
چکیده انگلیسی

We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization of the Cuntz–Pimsner C*-algebra to the context of subproduct systems. Suppose that X and Y are Arveson–Stinespring subproduct systems associated to two stochastic matrices over a countable set Ω  , and let T+(X)T+(X) and T+(Y)T+(Y) be their tensor algebras. We show that every algebraic isomorphism from T+(X)T+(X) onto T+(Y)T+(Y) is automatically bounded. Furthermore, T+(X)T+(X) and T+(Y)T+(Y) are isometrically isomorphic if and only if X and Y   are unitarily isomorphic up to a *-automorphism of ℓ∞(Ω)ℓ∞(Ω). When Ω   is finite, we prove that T+(X)T+(X) and T+(Y)T+(Y) are algebraically isomorphic if and only if there exists a similarity between X and Y   up to a *-automorphism of ℓ∞(Ω)ℓ∞(Ω). Moreover, we provide an explicit description of the Cuntz–Pimsner algebra O(X)O(X) in the case where Ω is finite and the stochastic matrix is essential.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 267, Issue 4, 15 August 2014, Pages 1057–1120
نویسندگان
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