کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11021717 | 1703049 | 2019 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An operator-valued Lyapunov theorem
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: An operator-valued Lyapunov theorem An operator-valued Lyapunov theorem](/preview/png/11021717.png)
چکیده انگلیسی
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weakâ-closed convex set of quantum effects (positive operators bounded above by the identity operator) under a sufficient condition on the non-injectivity of integration. To prove the operator-valued version of Lyapunov's theorem, we must first define the notions of essentially bounded, essential support, and essential range for quantum random variables (Borel measurable functions from a set to the bounded linear operators acting on a Hilbert space).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 469, Issue 1, 1 January 2019, Pages 117-125
Journal: Journal of Mathematical Analysis and Applications - Volume 469, Issue 1, 1 January 2019, Pages 117-125
نویسندگان
Sarah Plosker, Christopher Ramsey,