### Impacto

Llavona, José G. and Lacruz, Miguel
(1997)
*Composition operators between algebras of uniformly continuous functions.*
Archiv der Mathematik, 69
(1).
52-56 .
ISSN 0003-889X

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## Abstract

A characterization of uniform continuity for maps between unit balls of real Banach spaces is given in terms of universal properties. Also, it is shown that the classes

of compact and weakly compact composition operators induced by such maps agree.

Item Type: | Article |
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Uncontrolled Keywords: | Uniform continuity; Maps between unit balls of real Banach spaces; Universal properties; Compact and weakly compact composition operators |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16224 |

References: | R. M. ARON, J. GÓMEZ and J. G. LLAVONA, Homomorphisms between algebras of differentiable functions in infinite dimensions. Michigan Math. J. 35, 163 – 178 (1988). M. EIDELHEIT, Concerning rings of continuous functions. Ann. of Math. (2) 41, 391 – 393 (1940). M. GONZÁLEZ and J.M. GUTIÉRREZ, Compact and weakly compact homomorphisms between algebras of differentiable functions. Proc. Amer. Math. Soc. 115, 1025 – 1029 (1992). M. GONZÁLEZ and J. M. GUTIÉRREZ, Schauder type theorems for differentiable and holomorphic functions. Monatsh. Math., to appear. M. GONZÁLEZ and J. M. GUTIÉRREZ, Gantmacher type theorems for holomorphic mappings. Math. Nachr., to appear. J. JARAMILLO and J. G. LLAVONA, On the spectrum of C1b. E..Math. Ann.287, 531-538 (1990). H. KAMOWITZ, Compact endomorphisms of Banach algebras. Pacific J. Math. 89, 313 – 325 (1980). M. LINDSTRÖM and J. G. LLAVONA, Compact and weakly compact homomorphisms between algebras of continuous functions. J. Math. Anal. Appl. 166, 325 – 330 (1992). R. K. SINGH and W. H. SUMMERS, Compact and weakly compact composition operators on spaces of vector valued continuous functions. Proc. Amer. Math. Soc. 99, 667 – 670 (1987). |

Deposited On: | 10 Sep 2012 11:03 |

Last Modified: | 07 Feb 2014 09:25 |

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