LINEAR SUBSETS OF NONLINEAR SETS IN TOPOLOGICAL VECTOR SPACES

被引：198
作者：
Bernal-Gonzalez, Luis [1 ]
Pellegrino, Daniel [2 ]
Seoane-Sepulveda, Juan B. [3 ]
机构：
[1] Univ Seville, Dept Anal Matemat, Fac Matemat, E-41080 Seville, Spain
[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil
[3] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat, E-28040 Madrid, Spain
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 01期
关键词：
Lineability; spaceability; algebrability; real and complex analysis; special functions; operator theory; Baire category theorem; hypercyclic manifolds; zeros of polynomials; UNIVERSAL TAYLOR-SERIES; INVARIANT SUBSPACE PROBLEM; MAXIMAL CLUSTER SETS; BANACH-SPACES; HYPERCYCLIC OPERATORS; SIERPINSKI-ZYGMUND; REAL POLYNOMIALS; ALGEBRAIC GENERICITY; CLOSED SUBSPACES; LINEABILITY;
D O I：
10.1090/S0273-0979-2013-01421-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For the last decade there has been a generalized trend in mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis, operator theory, summability theory, polynomials in Banach spaces, hypercyclicity and chaos, and general functional analysis. This expository paper is devoted to providing an account on the advances and on the state of the art of this trend, nowadays known as lineability and spaceability.
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收藏
页码：71 / 130
页数：60
相关论文
共 274 条
  • [1] Functionals that do not attain their norm
    Acosta, Maria D.
    Aizpuru, Antonio
    Aron, Richard M.
    Garcia-Pacheco, Francisco J.
    [J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2007, 14 (03) : 407 - 418
  • [2] Aizpuru A, 2008, PUBL MATH-DEBRECEN, V72, P129
  • [3] Linear structure of sets of divergent sequences and series
    Aizpuru, A.
    Perez-Eslava, C.
    Seoane-Sepulveda, J. B.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (2-3) : 595 - 598
  • [4] Large structures in certain subsets of Orlicz spaces
    Akbarbaglu, I.
    Maghsoudi, S.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (11) : 4363 - 4373
  • [5] Porous sets and lineability of continuous functions on locally compact groups
    Akbarbaglu, Ibrahim
    Maghsoudi, Saeid
    Seoane-Sepulveda, Juan B.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 406 (01) : 211 - 218
  • [6] DISTRIBUTIONAL CHAOS FOR STRONGLY CONTINUOUS SEMIGROUPS OF OPERATORS
    Albanese, Angela A.
    Barrachina, Xavier
    Mangino, Elisabetta M.
    Peris, Alfredo
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (05) : 2069 - 2082
  • [7] The improper infinite derivatives of Takagi's nowhere-differentiable function
    Allaart, Pieter C.
    Kawamura, Kiko
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 372 (02) : 656 - 665
  • [8] [Anonymous], 1992, GRADUATE TEXTS MATH, DOI DOI 10.1007/978-1-4757-2189-8.109
  • [9] [Anonymous], 1952, Journal d'Analyse Mathematique, DOI DOI 10.1007/BF02786968
  • [10] [Anonymous], CAMBRIDGE TRACTS MAT
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