کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4617381 1339378 2012 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Determining elements in Banach algebras through spectral properties
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Determining elements in Banach algebras through spectral properties
چکیده انگلیسی

Let AA be a Banach algebra. By σ(x)σ(x) and r(x)r(x), we denote the spectrum and the spectral radius of x∈Ax∈A, respectively. We consider the relationship between elements a,b∈Aa,b∈A that satisfy one of the following two conditions: (1) σ(ax)=σ(bx)σ(ax)=σ(bx) for all x∈Ax∈A, (2) r(ax)≤r(bx)r(ax)≤r(bx) for all x∈Ax∈A. In particular, we show that (1) implies that a=ba=b if AA is a C∗C∗-algebra, and (2) implies that a∈Cba∈Cb if AA is a prime C∗C∗-algebra. As an application of the results concerning the conditions (1) and (2), we obtain some spectral characterizations of multiplicative maps.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 393, Issue 1, 1 September 2012, Pages 144–150
نویسندگان
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