Limits of vector functionals

被引：0

作者：

Archbold, RJ ^{[1
]}

Shah, MH ^{[1
]}

机构：

[1] Univ Aberdeen, Kings Coll, Dept Math Sci, Aberdeen AB24 3UE, Scotland

来源：

JOURNAL OF OPERATOR THEORY | 2001年 / 45卷 / 01期

关键词：

C*-algebra; vector functional; pure functional; antiliminal; prime;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For vector functionals on a C*-algebra of operators, we prove an analogue of Glimm's vector state space theorem. We deduce that a C*-algebra is prime and antiliminal if and only if the pure functionals are w*-dense in the unit ball of the dual. We also give a necessary and sufficient condition for a convex combination of inequivalent pure functionals to be a w*-limit of pure functionals.

引用

页码：39 / 51

页数：13

共 50 条

[1] Thin-Film Limits of Functionals on A-free Vector Fields
Kreisbeck, Carolin
Rindler, Filip
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2015, 64 (05) : 1383 - 1423
[2] Γ-LIMITS OF CONVOLUTION FUNCTIONALS
Lussardi, Luca
Magni, Annibale
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2013, 19 (02) : 486 - 515
[3] NORMS OF VECTOR FUNCTIONALS
Anoussis, M.
Ozawa, N.
Todorov, I. G.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (05) : 2057 - 2068
[4] ON GENERALIZED LIMITS + LINEAR FUNCTIONALS
ROBINSON, A
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1964, 14 (01) : 269 - &
[5] Γ-Limits of Functionals Determined by their Infima
Hafsa, Omar Anza
Mandallena, Jean Philippe
[J]. JOURNAL OF CONVEX ANALYSIS, 2016, 23 (01) : 103 - 137
[6] New results on Γ-limits of integral functionals
Ansini, Nadia
Dal Maso, Gianni
Zeppieri, Caterina Ida
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01): : 185 - 202
[7] GAMMA-LIMITS OF INTEGRAL FUNCTIONALS
BUTTAZZO, G
DALMASO, G
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1980, 37 : 145 - 185
[8] LIMITS OF FUNCTIONALS AND DIFFERENTIAL-OPERATORS
DEGIORGI, E
[J]. ASTERISQUE, 1981, (89-9) : 153 - 161
[9] LIMITS OF PURE FUNCTIONALS OF C*-ALGEBRAS
Shah, M. H.
[J]. JOURNAL OF OPERATOR THEORY, 2010, 63 (02) : 349 - 362
[10] STRICTLY POSITIVE FUNCTIONALS ON VECTOR LATTICES
VANCASTEREN, JA
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1979, 39 (JUL) : 51 - 72

← 1 2 3 4 5 →