کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5778438 1633769 2017 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Rigidity of composition operators on the Hardy space Hp
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Rigidity of composition operators on the Hardy space Hp
چکیده انگلیسی
Let ϕ be an analytic map taking the unit disk D into itself. We establish that the class of composition operators f↦Cϕ(f)=f∘ϕ exhibits a rather strong rigidity of non-compact behaviour on the Hardy space Hp, for 1≤p<∞ and p≠2. Our main result is the following trichotomy, which states that exactly one of the following alternatives holds: (i) Cϕ is a compact operator Hp→Hp, (ii) Cϕ fixes a (linearly isomorphic) copy of ℓp in Hp, but Cϕ does not fix any copies of ℓ2 in Hp, (iii) Cϕ fixes a copy of ℓ2 in Hp. Moreover, in case (iii) the operator Cϕ actually fixes a copy of Lp(0,1) in Hp provided p>1. We reinterpret these results in terms of norm-closed ideals of the bounded linear operators on Hp, which contain the compact operators K(Hp). In particular, the class of composition operators on Hp does not reflect the quite complicated lattice structure of such ideals.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 319, 15 October 2017, Pages 610-629
نویسندگان
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