Original Research

Absolutely summing multipliers and the Dvoretzky - Rogers theorem

J. H. Fourie
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 9, No 2 | a453 | DOI: https://doi.org/10.4102/satnt.v9i2.453 | © 1990 J. H. Fourie | This work is licensed under CC Attribution 4.0
Submitted: 05 July 1990 | Published: 05 July 1990

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J. H. Fourie,, South Africa

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Abstract

The space M(E) of absolutely summing multipliers of a Banach space E is considered. For some special types of Banach spaces E it turns out that M (E) can he characterized as an lᴾ-space of absolutely summable scalar sequences. We provide some important examples of Banach spaces for which the lᴾ-characterizations of M(E) hold true. The well known Dvoretzky-Rogers theorem plays an important role in these characterizations. An “alternative" version of the last men­tioned theorem is discussed.


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