Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

Abstract

LetF be aBK space withAK and $$\hat F$$ denote the set of all formal power series $$\hat f$$ with $$\hat f(z) = \sum\limits_{k = 0}^\infty {f_k z^k } $$ such that $$f = (f_k )_{k = 0}^\infty $$ e F for the sequence of coefficients of $$\hat f$$ . We give a necessary and sufficient condition for a point to be a bounded point evaluation on $$\hat F$$ , and for a polynomial to be cyclic in $$\hat F$$ . As special cases, we obtain the results for the space l p (β) in [7].