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.
Highlights
A b so lu tely sum m ing m u ltipliers unci the Dvore tz k y -Rogers theorem
H ierdie feit, asook die feit d at koordinaatsgewyse konvergensie en norm konvergensie in eindig-dim ensionele ruim tes saam val, lei to t die belangrike gevolgtrekking dat onvoorw aardelik konvergente reekse in eindig-dim ensionele ruim tes ook a b soluut konvergent is
D ie om gekeerde van hierdie bew ering is in die algem een nie geldig nie, m aar dit is egter tog w aar vir 'n groot klas van Banach-ruim tes
Summary
A b so lu tely sum m ing m u ltipliers unci the Dvore tz k y -Rogers theorem. The space M ( E ) o f absolutely sum m ing m ultipliers o f a Banaeh space E is considered. 'n Ry (.V,) in 'n B anach-ruim te E w ord sw ak ab so lu u t so m m eerbaar genoem as Z * , j j < oo vir elke a in die kontinue duaal E' van E. Dit is ’n B anach-ruim te met die norm :
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