Abstract
To continue our exposition, in particular, to prove the theorem of V. M. Kadets on the existence, in any infinite-dimensional Banach space, of series with nonlinear sum range, we need two theorems on the structure of infinite-dimensional spaces: Dvoretzky’s theorem on almost-Euclidean sections and Mazur’s theorem on basic sequences. Since these deep results are not incorporated in the standard functional analysis courses, their proof will be provided here in detail for the reader’s convenience.
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© 1997 Birkhäuser Verlag
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Kadets, M.I., Kadets, V.M. (1997). Some Results from the General Theory of Banach Spaces. In: Series in Banach Spaces. Operator Theory Advances and Applications, vol 94. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9196-7_7
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DOI: https://doi.org/10.1007/978-3-0348-9196-7_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9942-0
Online ISBN: 978-3-0348-9196-7
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