کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4620094 1339454 2009 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonlinear conditions for weighted composition operators between Lipschitz algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Nonlinear conditions for weighted composition operators between Lipschitz algebras
چکیده انگلیسی

Let T:Lip0(X)→Lip0(Y)T:Lip0(X)→Lip0(Y) be a surjective map between pointed Lipschitz ∗-algebras, where X and Y are compact metric spaces. On the one hand, we prove that if T satisfies the non-symmetric norm ∗-multiplicativity condition:‖T(f)T(g)¯−1‖∞=‖fg¯−1‖∞(f,g∈Lip0(X)), then T is of the formT(f)=τ⋅(η⋅(f○φ)+(1−η)⋅(f○φ)¯)(f∈Lip0(X)), where η and τ are functions on Y   such that η(Y)⊆{0,1}η(Y)⊆{0,1} and τ(Y)⊆{α∈K:|α|=1}, and φ:Y→X is a base point preserving Lipschitz homeomorphism. On the other hand, if T satisfies the weakly peripherally ∗-multiplicativity condition:Ranπ(fg¯)∩Ranπ(T(f)T(g)¯)≠∅(f,g∈Lip0(X)), where Ranπ(f)Ranπ(f) denotes the peripheral range of f, then T can be expressed asT(f)=τ⋅(f○φ)(f∈Lip0(X)), with τ and φ as above. As a consequence, we obtain similar descriptions for surjective maps between Lipschitz ∗-algebras Lip(X)Lip(X).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 359, Issue 1, 1 November 2009, Pages 1–14
نویسندگان
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