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Banach space valued Mean Periodic Functions.(Report)
- Article from:
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Tamsui Oxford Journal of Mathematical Sciences
- Article date:
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May 1, 2008
- Author:
- Navada, K. Gowri
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Copyright informationCOPYRIGHT 2008 Aletheia University. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Here we give a necessary and sufficient condition for a Banach space to be separable.
Keywords and Phrases: Mean periodic function, Vector valued measure.
For a Banach space B over the complex field C, let C(R, B) denote the set of all continuous functions defined on the real line R taking values in B with the compact convergence topology. When B = Cwe write C(R) for C(R, C). For a function [empty set] in C(R, B) let T ([empty set]) denote the closure in C(R, B) of the span of all translates of [empty set].
Definitiom 1. A function [empty set] in C(R, B) is said to be mean periodic if T ([empty set]) [not equal to] C(R, B).
We prove the following theorem.
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<[v.sub.i], m([b.sub.i])><[e.sub.n],[f.sub.n]*[mu]><[e.sub.n], [mu](b)><[e.sub.n], [integral] fd[mu]>
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empty set
The Concise Oxford Dictionary of Mathematics;
Christopher Clapham and James Nicholson;
21 words
...empty set The set, denoted by ∅︀, with no elements in it. Consequently, its cardinality , n (∅︀), is zero.
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