CLOSED UNIVERSAL SUBSPACES OF SPACES OF INFINITELY DIFFERENTIABLE FUNCTIONS

被引：4

作者：

Charpentier, Stephane ^{[1
]}

Menet, Quentin ^{[2
]}

Mouze, Augustin ^{[3
]}

机构：

[1] Univ Lille 1, Lab Paul Painleve, UMR 8524, F-59650 Villeneuve Dascq, France

[2] Univ Mons, Inst Math, B-7000 Mons, Belgium

[3] Lab Paul Painleve, UMR 8524, F-59651 Villeneuve Dascq, France

来源：

ANNALES DE L INSTITUT FOURIER | 2014年 / 64卷 / 01期

关键词：

infinitely differentiable real functions; spaceability; universality; universal series; Taylor series; HYPERCYCLIC SUBSPACES; FRECHET SPACE; SERIES; OPERATORS; THEOREM;

D O I：

10.5802/aif.2848

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We exhibit the first examples of Frechet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Frechet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Frechet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace of universal series in the Frechet space K-N.

引用

页码：297 / 325

页数：29

共 19 条

[1] Aron R., 2007, ADV COURSES MATH ANA, P1
[2] Abstract theory of universal series and applications
Bayart, F.
Grosse-Erdmann, K. -G.
Nestoridis, V.
Papadimitropoulos, C.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2008, 96 : 417 - 463
[3] Linearity of sets of strange functions
Bayart, F
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2005, 53 (02) : 291 - 303
[4] Hypercyclic subspaces in omega
Bès, J
Conejero, JA
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 316 (01) : 16 - 23
[5] Universal and chaotic multipliers on spaces of operators
Bonet, J
Martínez-Giménez, F
Peris, A
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 297 (02) : 599 - 611
[6] Bonet J, 2010, RACSAM REV R ACAD A, V104, P427, DOI 10.5052/RACSAM.2010.26
[7] Borel Emile, 1895, ANN SCI ECOLE NORM S, V12, P9, DOI DOI 10.24033/ASENS.406
[8] On the closed subspaces of universal series in Banach spaces and Frechet spaces
Charpentier, Stephane
[J]. STUDIA MATHEMATICA, 2010, 198 (02) : 121 - 145
[9] Universal families and hypercyclic operators
Grosse-Erdmann, KG
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (03) : 345 - 381
[10] KOMATSU H, 1973, J FAC SCI U TOKYO 1, V20, P25

← 1 2 →