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On Summing Multipliers and Applications

✍ Scribed by Shem Aywa; Jan H. Fourie

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
153 KB
Volume
253
Category
Article
ISSN
0022-247X

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✦ Synopsis

A scalar sequence ␣ is said to be a p-summing multiplier of a Banach space i ϱ 5

5 p E, if Ý ␣ x -ϱ for all weakly p-summable sequences in E. We study some

Ε½ . important properties of the space m E of all p-summing multipliers of E, p consider applications to E-valued operators on the sequence space l p , and extend this work to general ''summing multipliers.'' The case p s 1 shows close resem-Ε½ . blance to the work of B. Marchena and C. Pineiro Quaestiones Math., to appear , where the results originated from the authors' interest in sequences in the ranges of vector measures.

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