کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8959476 | 1646321 | 2018 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Convexity and star-shapedness of matricial range
ترجمه فارسی عنوان
محدب غشاء و ستاره ای محدوده ی ماتریسی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let A=(A1,â¦,Am) be an m-tuple of bounded linear operators acting on a Hilbert space H. Their joint (p,q)-matricial range Îp,q(A) is the collection of (B1,â¦,Bm)âMqm, where IpâBj is a compression of Aj on a pq-dimensional subspace. This definition covers various kinds of generalized numerical ranges for different values of p,q,m. In this paper, it is shown that Îp,q(A) is star-shaped if the dimension of H is sufficiently large. If dimâ¡H is infinite, we extend the definition of Îp,q(A) to Îâ,q(A) consisting of (B1,â¦,Bm)âMqm such that IââBj is a compression of Aj on a closed subspace of H, and consider the joint essential (p,q)-matricial rangeÎp,qess(A)=â{cl(Îp,q(A1+F1,â¦,Am+Fm)):F1,â¦,Fm are compact operators}. Both sets are shown to be convex, and the latter one is always non-empty and compact.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 9, 1 November 2018, Pages 2497-2515
Journal: Journal of Functional Analysis - Volume 275, Issue 9, 1 November 2018, Pages 2497-2515
نویسندگان
Pan-Shun Lau, Chi-Kwong Li, Yiu-Tung Poon, Nung-Sing Sze,