This is an announcement for the paper "Embeddings of M"{u}ntz spaces: composition operators" by S. Waleed Noor.

Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We discuss how properties of the embedding $M_\Lambda^2\subset L^2(\mu)$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$, have immediate consequences for composition operators on $M^2_\Lambda$. We give criteria for composition operators to be bounded, compact, or to belong to the Schatten--von Neumann ideals.

Archive classification: math.FA

Mathematics Subject Classification: 46E15, 46E20, 46E35

Citation: Integral Equations Operator Theory, Springer, 2012

Remarks: 15 Pages

Submitted from: waleed_math@hotmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.4719

or

http://arXiv.org/abs/1207.4719