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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embeddings of Müntz spaces: The Hilbertian case


Authors: S. Waleed Noor and Dan Timotin
Journal: Proc. Amer. Math. Soc. 141 (2013), 2009-2023
MSC (2010): Primary 46E15, 46E20, 46E35
Published electronically: December 18, 2012
MathSciNet review: 3034427
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Abstract: Given a strictly increasing sequence $ \Lambda =(\lambda _n)$ of nonnegative real numbers, with $ \sum _{n=1}^\infty \frac {1}{\lambda _n}<\infty $, the Müntz spaces $ M_\Lambda ^p$ are defined as the closure in $ L^p([0,1])$ of the monomials $ x^{\lambda _n}$. We discuss properties of the embedding $ M_\Lambda ^p\subset L^p(\mu )$, where $ \mu $ 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.


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Additional Information

S. Waleed Noor
Affiliation: Abdus Salam School of Mathematical Sciences, New Muslim Town, Lahore, 54600, Pakistan
Email: waleed{\textunderscore}math@hotmail.com

Dan Timotin
Affiliation: Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, Bucharest, Romania
Email: Dan.Timotin@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11681-8
PII: S 0002-9939(2012)11681-8
Keywords: Müntz space, embedding measure, lacunary sequence, Schatten–von Neumann classes
Received by editor(s): September 18, 2011
Published electronically: December 18, 2012
Communicated by: Richard Rochberg
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.