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A nonstandard density theorem for weak topologies on Banach and Bochner spaces
Author(s) -
Vanderputten Laurent
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310027
Subject(s) - mathematics , bochner space , banach space , class (philosophy) , pure mathematics , context (archaeology) , measure (data warehouse) , integrable system , eberlein–šmulian theorem , convergence (economics) , space (punctuation) , discrete mathematics , lp space , computer science , paleontology , database , artificial intelligence , economics , biology , economic growth , operating system
Abstract We prove a nonstandard density result. It asserts that if a particular formula is true for functions in a set K of linear continuous functions between Banach spaces E and D , then it remains valid for functions that are limits, in the uniform convergence topology on a given class ℳ of subsets of E , of nets of vectors in K . We then apply this result to various class ℳ and sets K in the context of E ‐valued Bochner integrable functions defined on a finite measure space.