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.

引用

页码：71 / 130

页数：60

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