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 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.
Citation
F. J. Garc´la-Pacheco. M. Mart´ln. J. B. Seoane-Sep´ulveda. "LINEABILITY, SPACEABILITY, AND ALGEBRABILITY OF CERTAIN SUBSETS OF FUNCTION SPACES." Taiwanese J. Math. 13 (4) 1257 - 1269, 2009. https://doi.org/10.11650/twjm/1500405506
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