کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591345 1335024 2012 69 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Free biholomorphic functions and operator model theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Free biholomorphic functions and operator model theory
چکیده انگلیسی

Let f=(f1,…,fn)f=(f1,…,fn) be an n  -tuple of formal power series in noncommutative indeterminates Z1,…,ZnZ1,…,Zn such that f(0)=0f(0)=0 and the Jacobian detJf(0)≠0, and let g=(g1,…,gn)g=(g1,…,gn) be its inverse with respect to composition. We assume that f and g have nonzero radius of convergence and g   is a bounded free holomorphic function on the open unit ball [Bn(H)]1[B(H)n]1, where B(H)B(H) is the algebra of bounded linear operators an a Hilbert space HH. In this paper, several results concerning the noncommutative multivariable operator theory on the unit ball [B(H)n]1− are extended to the noncommutative domainBf(H):={X∈Bn(H):g(f(X))=X and ‖f(X)‖⩽1}Bf(H):={X∈B(H)n:g(f(X))=X and ‖f(X)‖⩽1} for an appropriate evaluation X↦f(X)X↦f(X). We develop an operator model theory and dilation theory for Bf(H)Bf(H), where the associated universal model is an n  -tuple (MZ1,…,MZn)(MZ1,…,MZn) of left multiplication operators acting on a Hilbert space H2(f)H2(f) of formal power series. All the results of this paper have commutative versions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 262, Issue 7, 1 April 2012, Pages 3240–3308
نویسندگان
,