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An inequality for Cauchy products


Author: Javad Mashreghi
Journal: Proc. Amer. Math. Soc. 145 (2017), 3013-3016
MSC (2010): Primary 47A30; Secondary 26D15, 47A63
DOI: https://doi.org/10.1090/proc/13437
Published electronically: December 8, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that $ \ell ^p$ is closed under the Cauchy product by $ \ell ^1$ sequences.


References [Enhancements On Off] (What's this?)

  • [1] Raymond Cheng and William T. Ross, An inner-outer factorization in $ \ell ^p$ with applications to ARMA processes, J. Math. Anal. Appl. 437 (2016), no. 1, 396-418. MR 3451972, https://doi.org/10.1016/j.jmaa.2016.01.009
  • [2] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • [3] Javad Mashreghi, Representation theorems in Hardy spaces, London Mathematical Society Student Texts, vol. 74, Cambridge University Press, Cambridge, 2009. MR 2500010

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Additional Information

Javad Mashreghi
Affiliation: Université Laval, Département de mathématiques et de statistique, Québec City, Québec, G1V 0A6, Canada
Email: javad.mashreghi@mat.ulaval.ca

DOI: https://doi.org/10.1090/proc/13437
Received by editor(s): May 3, 2016
Received by editor(s) in revised form: August 15, 2016
Published electronically: December 8, 2016
Additional Notes: This work was supported by NSERC (Canada).
Communicated by: Stephen Ramon Garcia
Article copyright: © Copyright 2016 American Mathematical Society

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