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

被引：32

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

共 19 条

[1] Lineability and spaceability of sets of functions on R [J].

Aron, R ;

Gurariy, VI ;

Seoane, JB .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (03) :795-803

[2]

ARON R, 2001, REV REAL ACAD CIEN A, V95, P7

[3] Algebrability of the set of everywhere surjective functions on C [J].

Aron, Richard M. ;

Seoane-Sepulveda, Juan B. .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2007, 14 (01) :25-31

[4] Algebrability of the set of non-convergent Fourier series [J].

Aron, Richard M. ;

Perez-Garcia, David ;

Seoane-Sepulveda, Juan B. .

STUDIA MATHEMATICA, 2006, 175 (01) :83-90

[5] Algebras in sets of queer functions [J].

Bayart, Frederic ;

Quarta, Lucas .

ISRAEL JOURNAL OF MATHEMATICS, 2007, 158 (01) :285-296

[6]

ENFLO P, LINEABILITY SPACEABI

[7]

Fonf V. P., 1999, C R ACAD BULGARE SCI, V52, P13

[8]

GARCIA D, INFINITE DIMENSIONAL

[9] Lineability and algebrability of pathological phenomena in analysis [J].

Garcia-Pacheco, F. J. ;

Palmberg, N. ;

Seoane-Sepulveda, J. B. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 326 (02) :929-939

[10]

Gelbaum B.R., 2003, Counterexamples in analysis

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