Linear maps transforming the higher numerical ranges
نویسندگان
چکیده
منابع مشابه
Linear maps transforming the higher numerical ranges
Let k ∈ {1, . . . , n}. The k-numerical range of A ∈Mn is the set Wk(A) = {(trX∗AX)/k : X is n× k, X∗X = Ik}, and the k-numerical radius of A is the quantity wk(A) = max{|z| : z ∈ Wk(A)}. Suppose k > 1, k′ ∈ {1, . . . , n′} and n′ < C(n, k)min{k′, n′ − k′}. It is shown that there is a linear map φ : Mn → Mn′ satisfying Wk′(φ(A)) = Wk(A) for all A ∈ Mn if and only if n′/n = k′/k or n′/n = k′/(n−...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.11.026