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)
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
Given a sequence of bounded operators aj on a Hilbert space H with âj=1âajâaj=1=âj=1âajajâ, we study the map Ψ defined on B(H) by Ψ(x)=âj=1âajâxaj and its restriction Φ to the Hilbert-Schmidt class C2(H). In the case when the sum âj=1âajâaj is norm-convergent we show in particular that the operator Φâ1 is not invertible if and only if the Câ-algebra A generated by {aj}j=1â has an amenable trace. This is used to show that Ψ may have fixed points in B(H) which are not in the commutant Aâ² 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 Aâ² 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
Journal: Journal of Mathematical Analysis and Applications - Volume 389, Issue 2, 15 May 2012, Pages 1291-1302
نویسندگان
Bojan Magajna,