Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces
HTML articles powered by AMS MathViewer

by Daniel Azagra, Robb Fry and Alejandro Montesinos PDF
Proc. Amer. Math. Soc. 133 (2005), 727-734 Request permission

Abstract:

We show that if $Y$ is a separable subspace of a Banach space $X$ such that both $X$ and the quotient $X/Y$ have $C^p$-smooth Lipschitz bump functions, and $U$ is a bounded open subset of $X$, then, for every uniformly continuous function $f:Y\cap U\to \mathbb {R}$ and every $\varepsilon >0$, there exists a $C^p$-smooth Lipschitz function $F:X\to \mathbb {R}$ such that $|F(y)-f(y)|\leq \varepsilon$ for every $y\in Y\cap U$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20
  • Retrieve articles in all journals with MSC (2000): 46B20
Additional Information
  • Daniel Azagra
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
  • Email: daniel_azagra@mat.ucm.es
  • Robb Fry
  • Affiliation: Department of Mathematics and Computer Science, St. Francis Xavier University, P.O. Box 5000, Antigonish, Nova Scotia, Canada B2G 2W5
  • Email: rfry@stfx.ca
  • Alejandro Montesinos
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
  • Email: a_montesinos@mat.ucm.es
  • Received by editor(s): January 26, 2003
  • Published electronically: October 21, 2004
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 727-734
  • MSC (2000): Primary 46B20
  • DOI: https://doi.org/10.1090/S0002-9939-04-07715-9
  • MathSciNet review: 2113921