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Banach Spaces with the Riemann–Lebesgue or the Analytic Riemann–Lebesgue Property
Author(s) -
Bu Shangquan,
Chill Ralph
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001182
Subject(s) - mathematics , lebesgue integration , lp space , pure mathematics , lebesgue's number lemma , riemann integral , eberlein–šmulian theorem , banach space , riemann–stieltjes integral , class (philosophy) , interpolation space , lebesgue–stieltjes integration , mathematical analysis , functional analysis , integral equation , operator theory , fourier integral operator , biochemistry , chemistry , artificial intelligence , computer science , gene
In this note, two geometric properties of Banach spaces are proposed and discussed, related to the validity of the lemma of Riemann–Lebesgue in spaces of weakly integrable functions. The class of Banach spaces with the analytic Riemann–Lebesgue property is shown to be precisely the class of Banach spaces for which a weak form of a theorem of Ingham holds. 2000 Mathematics Subject Classification 42A75, 45N05, 47D05.