کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896739 | 1630599 | 2018 | 49 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multiplier algebras of complete Nevanlinna-Pick spaces: Dilations, boundary representations and hyperrigidity
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study reproducing kernel Hilbert spaces on the unit ball with the complete Nevanlinna-Pick property through the representation theory of their algebras of multipliers. We give a complete description of the representations in terms of the reproducing kernels. While representations always dilate to â-representations of the ambient Câ-algebra, we show that in our setting we automatically obtain coextensions. In fact, we show that in many cases, this phenomenon characterizes the complete Nevanlinna-Pick property. We also deduce operator theoretic dilation results which are in the spirit of work of Agler and several other authors. Moreover, we identify all boundary representations, compute the Câ-envelopes and determine hyperrigidity for certain analogues of the disc algebra. Finally, we extend these results to spaces of functions on homogeneous subvarieties of the ball.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 274, Issue 6, 15 March 2018, Pages 1690-1738
Journal: Journal of Functional Analysis - Volume 274, Issue 6, 15 March 2018, Pages 1690-1738
نویسندگان
Raphaël Clouâtre, Michael Hartz,