Rendiconti del Circolo Matematico di Palermo

, Volume 49, Issue 1, pp 115–120 | Cite as

On the spacel P(β)

  • B. Yousefi


Let\(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel P(β) of all power series\(f(z) = \sum\limits_{n = 0}^\infty {\hat f(n)z^n } \) such that\(\sum\limits_{n = 0}^\infty {|\hat f(n)|^p |\beta (n)|^p } \). We give a necessary and sufficient condition for a polynomial to be cyclic inl P(β) and a point to be bounded point evaluation onl P(β).

AMS Subject Classification

Primary 47B37 Secondary 47A25 

Keywords and phrases

Invariant subspaces lattice The Banach space of formal power series associated with a sequenceβ Cyclic vctor reproducing kernel bounded point evaluation 


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    Shields A.L.,Weighted shift operators and analytic function theory, Math. Survey, A.M.S. Providenc,13 (1974), 49–128.MathSciNetGoogle Scholar

Copyright information

© Springer 2000

Authors and Affiliations

  • B. Yousefi
    • 1
  1. 1.Dept. of Math. College of SciencesShiraz UniversityShirazIran

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