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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ c_0$-subspaces and fourth dual types


Author: Vasiliki A. Farmaki
Journal: Proc. Amer. Math. Soc. 102 (1988), 321-328
MSC: Primary 46B20,; Secondary 46B10
DOI: https://doi.org/10.1090/S0002-9939-1988-0920994-X
MathSciNet review: 920994
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Abstract: For a separable Banach space $ X$, we define the notion of a $ {c_{0 + }}$-type on $ X$ and show that the existence of such a type is equivalent to the embeddability of $ {c_0}$ in $ X$. All these types are weakly null and fourth dual (i.e. of the form $ \tau (x) = \left\Vert {x + g} \right\Vert$ for $ g \in {X^{****}}$). We define the $ {l^{{l^ + }}}$-dual types on $ X$ (these are generated by sequences in $ {X^{**}}$) and prove that they coincide with the fourth dual types on $ X$. We also prove that $ {c_{0 + }}$-types are fourth dual types.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0920994-X
Keywords: Types on Banach spaces, $ {c_{0 + }}$-types, weakly null types, $ {l^{{l^ + }}}$-dual types, fourth dual types, generation of types, isomorphic embedding
Article copyright: © Copyright 1988 American Mathematical Society