کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904936 | 1633760 | 2018 | 38 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Composition operators with a minimal commutant
ترجمه فارسی عنوان
اپراتورهای ترکیب با کمترین تعویض
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کلمات کلیدی
اپراتور ترکیب فضای هاردی، نقشه خطی خطی، اپراتور با حداقل تعویض،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
Let CÏ be a composition operator on the Hardy space H2, induced by a linear fractional self-map Ï of the unit disk. We consider the question whether the commutant of CÏ is minimal, in the sense that it reduces to the weak closure of the unital algebra generated by CÏ. We show that this happens in exactly three cases: when Ï is either a non-periodic elliptic automorphism, or a parabolic non-automorphism, or a loxodromic self-map of the unit disk. Also, we consider the case of a composition operator induced by a univalent, analytic self-map Ï of the unit disk that fixes the origin and that is not necessarily a linear fractional map, but in exchange its Königs's domain is bounded and strictly starlike with respect to the origin, and we show that the operator CÏ has a minimal commutant. Furthermore, we provide two examples of univalent, analytic self-maps Ï of the unit disk such that CÏ is compact but it fails to have a minimal commutant.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 328, 13 April 2018, Pages 890-927
Journal: Advances in Mathematics - Volume 328, 13 April 2018, Pages 890-927
نویسندگان
Miguel Lacruz, Fernando León-Saavedra, Srdjan Petrovic, Luis RodrÃguez-Piazza,