MULTIPLES OF HYPERCYCLIC OPERATORS

作者：Badea Catalin^*; Grivaux Sophie; Muller Vladimir

来源：Proceedings of the American Mathematical Society, 2009, 137(4): 1397-1403.

• Hypercyclic operators
• bilateral weighted shifts

We give a negative answer to a question of Prajitura by showing that there exists an invertible bilateral weighted shift T on l(2)(Z) such that T and 3T are hypercyclic but 2T is not. Moreover, any G(delta) set M subset of (0,infinity) which is bounded and bounded away from zero can be realized as M = {t > 0 | tT is hypercyclic} for some invertible operator T acting on a Hilbert space.

• 出版日期2009