کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9495477 1335132 2005 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Birkhoff's theorem and multidimensional numerical range
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Birkhoff's theorem and multidimensional numerical range
چکیده انگلیسی
We show that, under certain conditions, Birkhoff's theorem on doubly stochastic matrices remains valid for countable families of discrete probability spaces which have nonempty intersections. Using this result, we study the relation between the spectrum of a self-adjoint operator A and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the operator A. Every collection of eigenvalues which can be obtained by the Rayleigh-Ritz formula generates an extreme point of the multidimensional numerical range. However, it may also have other extreme points.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 222, Issue 1, 1 May 2005, Pages 61-97
نویسندگان
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