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Lineability, spaceability, and algebrability of certain subsets of function spaces.

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García-Pacheco, F.J. and Martín, M. and Seoane-Sepúlveda, Juan B. (2009) Lineability, spaceability, and algebrability of certain subsets of function spaces. Taiwanese Journal of Mathematics, 13 (4). pp. 1257-1269. ISSN 1027-5487

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Official URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/463/349


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Abstract

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 Riemann-integrable; 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.


Item Type:Article
Uncontrolled Keywords:Riemann integrable; Lebesgue integrable; Continuous unbounded functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20032
Deposited On:21 Feb 2013 15:24
Last Modified:25 Nov 2016 12:45

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