کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602022 1631163 2009 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonlinear maps preserving numerical radius of indefinite skew products of operators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Nonlinear maps preserving numerical radius of indefinite skew products of operators
چکیده انگلیسی

Let H be a complex Hilbert space of dimension greater than 2 and J∈B(H) be an invertible self-adjoint operator. Denote by A†=J-1A∗J the indefinite conjugate of A∈B(H) with respect to J and denote by w(A) the numerical radius of A. Let W and V be subsets of B(H) which contain all rank one operators, and let Φ:W→V be a surjective map. We show that Φ satisfies w(AB†)=w(Φ(A)Φ(B)†) and w(A†B)=w(Φ(A)†Φ(B)) for all A,B∈W if and only if there exist scalars ϵi∈{-1,1} (i=1,2), unitary (or conjugate unitary) operators U, V on H satisfying U†U=ϵ1I, V†V=ϵ2I and a functional φ:W→C with |φ(A)|≡1 such that Φ(A)=φ(A)UAV for all A∈W; Φ satisfies w(AB†A)=w(Φ(A)Φ(B)†Φ(A)) for all A,B∈W if and only if either there exist ϵ∈{-1,1}, a unitary (or conjugate unitary) operator U on H satisfying U†U=ϵI and a functional φ:W→C with |φ(A)|≡1 such that Φ(A)=φ(A)UAU∗ for all A∈W; or, there exist a nonzero real number b, a unitary (or conjugate unitary) operator U on H satisfying U∗JU=bJ-1 and a functional φ:W→C with |φ(A)|≡1 such that Φ(A)=φ(A)UA∗U∗ for all A∈W.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 430, Issues 8–9, 15 April 2009, Pages 2240-2253