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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
A bounded linear operator T:H1âH2, where H1,H2 are Hilbert spaces is said to be norm attaining if there exists a unit vector xâH1 such that âTxâ=âTâ. If for any closed subspace M of H1, the restriction T|M:MâH2 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
Journal: Journal of Mathematical Analysis and Applications - Volume 465, Issue 1, 1 September 2018, Pages 547-556
نویسندگان
G. Ramesh,