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Given a strictly increasing sequence Λ = (λn) of nonegative real numbers, with ∞ n=1 1 λn < ∞, the Müntz spaces M p Λ are defined as the closure in L p ([0, 1]) of the monomials x λn . We discuss properties of the embedding M p Λ ⊂ L p (µ), where µ is a finite positive Borel measure on the interval [0, 1]. Most of the results are obtained for the Hilbertian case p = 2, in which we give conditions for the embedding to be bounded, compact, or to belong to the Schatten-von Neumann ideals.2010 Mathematics Subject Classification. 46E15, 46E20, 46E35.

In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators C φ f = f • φ induced by affine self-maps φ of the right half-plane C + on the Hardy-Hilbert space H 2 (C + ). The interplay between complex symmetry and cyclicity plays a key role in the analysis. We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodríguez.2010 Mathematics Subject Classification. Primary 47B33, 47A16, 47B32.

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Suppose H is a weighted Hardy space of analytic functions on the unit ball B n ⊂ C n such that the composition operator C ψ defined byIf ϕ is an involutive Moebius automorphism of B n , we find a conjugation operator J on H such that C ϕ = J C * ϕ J . The case n = 1 answers a question of Garcia and Hammond.