LINEABILITY, SPACEABILITY, AND ALGEBRABILITY OF CERTAIN SUBSETS OF FUNCTION SPACES

被引：31

作者：

Garcia-Pacheco, F. J. ^{[1
]}

Martin, M. ^{[2
]}

Seoane-Sepulveda, J. B. ^{[3
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

[3] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat, E-28040 Madrid, Spain

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2009年 / 13卷 / 04期

关键词：

Riemann integrable; Lebesgue integrable; Continuous unbounded functions; Lineability; Spaceability; Algebrability; BANACH-SPACES; SUBSPACES; SETS;

D O I：

10.11650/twjm/1500405506

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1257 / 1269

页数：13

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