On the Geometry of Müntz Spaces

Let λ = { k } k = 1 ∞ satisfy 0 < 1 < 2 <,k = 1 ∞ 1 / k < ∞ and i n f k ( k + 1 - k) > 0. we investigate the müntz spaces m p λ = span ¯ { t k: k = 1,2,. } ⊂ l p (0,1) for 1 ≤ p ≤ ∞. we show that,for each p,there is a müntz space f p which contains isomorphic copies of all müntz spaces as complemented subspaces. f p is uniquely determined up to isomorphisms by this maximality property. we discuss explicit descriptions of f p. in particular f p is isomorphic to a müntz space m p (λ ^) where λ ^ consists of positive integers. finally we show that the banach spaces (n f n) p for 1 ≤ p < ∞ and (n f n) 0 for p = ∞ are always isomorphic to suitable müntz spaces m p (λ) if the f n are the spans of arbitrary finitely many monomials over [ 0,1 ]. © 2015 sergey v. ludkovsky and wolfgang lusky.