Open Access
1999/2000 Functions Preserving Sequence Spaces
Raymond J. Grinnell
Real Anal. Exchange 25(1): 239-256 (1999/2000).


Let $A$ and $B$ be sets of real sequences. Let $F(A,B)$ denote the set of functions $f : \R \rightarrow \R$ that preserve $A$ and $B$ in the sense that $(f(a_{n})) \in B$ for all sequences $(a_{n}) \in A.$ These functions are generalizations of convergence preserving functions first introduced by Rado. We establish identities and inclusions for $F(A,B)$ when $A$ and $B$ are $l^{p}$-spaces and other well-known sequence spaces. We also characterize $F(A,B)$ in terms of elementary classes of functions. Our characterizations are motivated by the work of Bors\'{\i}k, \v{C}erve\v{n}ansk\'{y} and \v{S}al\'{a}t.


Download Citation

Raymond J. Grinnell. "Functions Preserving Sequence Spaces." Real Anal. Exchange 25 (1) 239 - 256, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 0937.40500
MathSciNet: MR1758005

Primary: 26A99 , 40A05 , 46A45

Keywords: Function preserving convergence , infinite series , sequence space

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
Back to Top