کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9498236 | 1631200 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multiplicative preservers and induced operators
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
Let V be an n-dimensional Hilbert space. Suppose H is a subgroup of the symmetric group of degree m, and Ï:HâC is a character of degree 1 on H. Consider the symmetrizer on the tensor space âmVS(v1ââ¯âvm)=1|H|âÏâHÏ(Ï)vÏ-1(1)ââ¯âvÏ-1(m)defined by H and Ï. The subspace VÏm(H) of âmV spanned by S(âmV) is called the symmetry class of tensors over V associated with H and Ï. The elements in VÏm(H) of the form S(v1 â â¯Â â vm) are called decomposable tensors and are denoted by v1 â â¯Â â vm. For any linear operator T acting on V, there is an (unique) induced operator KÏ(T) (or just K(T) for notational simplicity) acting on VÏm(H) satisfyingK(T)v1ââ¯âvm=Tv1ââ¯âTvm.We characterize multiplicative maps Ï such that F(Ï(T)) = F(T) for all operators T acting on V, where F are various scalar or set valued functions including the spectral radius, (decomposable) numerical radius, spectral norm, spectrum, (decomposable) numerical range of T or K(T).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 401, 15 May 2005, Pages 307-323
Journal: Linear Algebra and its Applications - Volume 401, 15 May 2005, Pages 307-323
نویسندگان
Wai-Shun Cheung, M. Antonia Duffner, Chi-Kwong Li,