Spectral theory in ordered Banach algebras

被引:7
作者
Mouton, Sonja [1 ]
Raubenheimer, Heinrich [2 ]
机构
[1] Stellenbosch Univ, Dept Math Sci, Private Bag X1, ZA-7602 Matieland, South Africa
[2] Univ Johannesburg, Dept Math, POB 524, ZA-2006 Auckland Pk, South Africa
关键词
Ordered Banach algebra; Spectral theory; COMPACT-OPERATORS; FREDHOLM THEORY; POSITIVE OPERATORS; ELEMENTS; CONTINUITY; LATTICES; DOMINATION;
D O I
10.1007/s11117-016-0440-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We give a survey of the development of the spectral theory in ordered Banach algebras; from its roots in operator theory to the modern abstract context.
引用
收藏
页码:755 / 786
页数:32
相关论文
共 67 条
[1]   Some properties of essential spectra of a positive operator [J].
Alekhno, Egor A. .
POSITIVITY, 2007, 11 (03) :375-386
[2]   The irreducibility in ordered Banach algebras [J].
Alekhno, Egor A. .
POSITIVITY, 2012, 16 (01) :143-176
[3]   Some properties of essential spectra of a positive operator, II [J].
Alekhno, Egor A. .
POSITIVITY, 2009, 13 (01) :3-20
[4]  
Aliprantis C.D., 2010, Positive operators
[5]   POSITIVE COMPACT OPERATORS ON BANACH-LATTICES [J].
ALIPRANTIS, CD ;
BURKINSHAW, O .
MATHEMATISCHE ZEITSCHRIFT, 1980, 174 (03) :289-298
[6]   ON THE O-SPECTRUM OF REGULAR OPERATORS AND THE SPECTRUM OF MEASURES [J].
ARENDT, W .
MATHEMATISCHE ZEITSCHRIFT, 1981, 178 (02) :271-287
[7]   SPECTRUM PRESERVING LINEAR MAPPING SIN BANACH-ALGEBRAS [J].
AUPETIT, B ;
MOUTON, HDT .
STUDIA MATHEMATICA, 1994, 109 (01) :91-100
[8]  
Aupetit B., 1991, A Primer on Spectral Theory
[9]   On domination of inessential elements in ordered Banach algebras [J].
Behrendt, D. ;
Raubenheimer, H. .
ILLINOIS JOURNAL OF MATHEMATICS, 2007, 51 (03) :927-936
[10]   The upper Browder spectrum property [J].
Benjamin, Ronalda ;
Mouton, Sonja .
POSITIVITY, 2017, 21 (02) :575-592