کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899524 1631546 2018 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Absolutely norm attaining paranormal operators
ترجمه فارسی عنوان
کاملا طبیعی برای دستیابی به اپراتورهای پارانورال
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
A bounded linear operator T:H1→H2, where H1,H2 are Hilbert spaces is said to be norm attaining if there exists a unit vector x∈H1 such that ‖Tx‖=‖T‖. If for any closed subspace M of H1, the restriction T|M:M→H2 of T to M is norm attaining, then T is called an absolutely norm attaining operator or AN-operator. We prove the following characterization theorem: a positive operator T defined on an infinite dimensional Hilbert space H is an AN-operator if and only if the essential spectrum of T is a single point and [m(T),me(T)) contains atmost finitely many points. Here m(T) and me(T) are the minimum modulus and essential minimum modulus of T, respectively. As a consequence we obtain a sufficient condition under which the AN-property of an operator implies AN-property of its adjoint. We also study the structure of paranormal AN-operators and give a necessary and sufficient condition under which a paranormal AN-operator is normal.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 465, Issue 1, 1 September 2018, Pages 547-556
نویسندگان
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