کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419299 1339390 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fixed points of normal completely positive maps on B(H)
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Fixed points of normal completely positive maps on B(H)
چکیده انگلیسی

Given a sequence of bounded operators aj on a Hilbert space H with ∑j=1∞aj⁎aj=1=∑j=1∞ajaj⁎, we study the map Ψ defined on B(H) by Ψ(x)=∑j=1∞aj⁎xaj and its restriction Φ to the Hilbert-Schmidt class C2(H). In the case when the sum ∑j=1∞aj⁎aj is norm-convergent we show in particular that the operator Φ−1 is not invertible if and only if the C⁎-algebra A generated by {aj}j=1∞ has an amenable trace. This is used to show that Ψ may have fixed points in B(H) which are not in the commutant A′ of A even in the case when the weak* closure of A is injective. However, if A is abelian, then all fixed points of Ψ are in A′ even if the operators aj are not positive.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 389, Issue 2, 15 May 2012, Pages 1291-1302
نویسندگان
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