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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nests of subspaces in Banach space and their order types

Authors: Alvaro Arias and Jeff Farmer
Journal: Trans. Amer. Math. Soc. 331 (1992), 113-130
MSC: Primary 46B20
MathSciNet review: 1050084
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Abstract: This paper addresses some questions which arise naturally in the theory of nests of subspaces in Banach space. The order topology on the index set of a nest is discussed, as well as the method of spatial indexing by a vector; sufficient geometric conditions for the existence of such a vector are found. It is then shown that a continuous nest exists in any Banach space.

Applications and examples follow; in particular, an extension of the Volterra nest in $ {L^\infty }[ {0,1} ]$ to a continuous one, a continuous nest in a Banach space having no two elements isomorphic to one another, and a characterization of separable $ {\mathcal{L}_p}$-spaces in terms of nests.

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Article copyright: © Copyright 1992 American Mathematical Society