کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4618581 1339414 2011 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Common hypercyclic vectors for the conjugate class of a hypercyclic operator
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Common hypercyclic vectors for the conjugate class of a hypercyclic operator
چکیده انگلیسی

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense Gδ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense Gδ set. As a corollary, the hypercyclic operators on such a Banach space form a connected subset of the operator algebra with the strong operator topology.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 375, Issue 1, 1 March 2011, Pages 139-148