Taiwanese Journal of Mathematics


F. J. Garc´la-Pacheco, M. Mart´ln, and J. B. Seoane-Sep´ulveda

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We construct infinite-dimensional Banach spaces and infinitely generated Banach algebras of functions that, except for 0, satisfy some kind of special or pathological property. Three of these structures are: a Banach algebra of everywhere continuous bounded functions which are not Riemannintegrable ; a Banach space of Lebesgue-integrable functions that are not Riemann-integrable; an algebra of continuous unbounded functions defined on an arbitrary non-compact metric space.

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Taiwanese J. Math., Volume 13, Number 4 (2009), 1257-1269.

First available in Project Euclid: 18 July 2017

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Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 46E25: Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
Secondary: 15A03: Vector spaces, linear dependence, rank 26A30: Singular functions, Cantor functions, functions with other special properties 54C30: Real-valued functions [See also 26-XX]

Riemann integrable Lebesgue integrable continuous unbounded functions lineability spaceability algebrability


Garc´la-Pacheco, F. J.; Mart´ln, M.; Seoane-Sep´ulveda, J. B. LINEABILITY, SPACEABILITY, AND ALGEBRABILITY OF CERTAIN SUBSETS OF FUNCTION SPACES. Taiwanese J. Math. 13 (2009), no. 4, 1257--1269. doi:10.11650/twjm/1500405506. https://projecteuclid.org/euclid.twjm/1500405506

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