tailieunhanh - Báo cáo hóa học: " On the eleventh question of Allen Shields"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: On the eleventh question of Allen Shields | Yousefi and Kashkooly Fixed Point Theory and Applications 2011 2011 16 http content 2011 1 16 RESEARCH Fixed Point Theory and Applications a SpringerOpen Journal Open Access On the eleventh question of Allen Shields Bahmann Yousefi1 and Ali Iloon Kashkooly2 Correspondence b_yousefi@pnu. department of Mathematics Payame Noor University . Box 7W55-1368 Shiraz Iran Full list of author information is available at the end of the article Abstract In this article we will give sufficient conditions for the boundedness of the analytic projection on the set of multipliers of the formal Laurent series spaces. This answers a question that has been raised by A. L. Shields. Also we will characterize the fixed points of some weighted composition operators acting on weighted Hardy spaces. AMS Subject Classification Primary 47B37 Secondary 47B38. Keywords Banach space of Laurent series associated with a sequence p bounded point evaluation spectral set weak operator topology 1 Introduction Let fi n TO -TO be a sequence of positive numbers satisfying b 0 1. If 1 p TO then TO the space Lp b consists of all formal Laurent series f z f n zn such that the n -TO norm f p f fi n -TO lf n lpfi n p is finite. When n just runs over N u 0 the TO 2 space Lp b only contains formal power series f z 52 f n zn and it is usually denoted n 0 by Hp b . These spaces are also called as weighted Hardy spaces. If p 2 such spaces were introduced by Allen L. Shields to study weighted shift operators in his article 1 which is one of basic studies in this area and is a pretty large study that contains a number of interesting results and indeed it is mainly of auxiliary nature. Actually Shields showed a close relation between injective weighted shifts and the multiplication operator Mz acting on L2 b or H2 b see 1 Proposition 7 . These are reflexive Banach spaces with the norm - p. Let fk n 3k n . Hence fk z z and ftUez is a basis for Lp b such that fk b k . .