Finite generation in C*-algebras and Hilbert C*-modules

被引：5
作者：
Blecher, David P. [1 ]
Kania, Tomasz [2 ,3 ]
机构：
[1] Univ Houston, Dept Math, Houston, TX 77204 USA
[2] Polish Acad Sci, Inst Math, PL-00656 Warsaw, Poland
[3] Univ Lancaster, Fylde Coll, Dept Math & Stat, Lancaster LA1 4YF, England
来源：
STUDIA MATHEMATICA | 2014年 / 224卷 / 02期
基金：
美国国家科学基金会;
关键词：
Hilbert module; C*-module; finitely generated ideal; algebraically finitely generated; maximal ideal; C*-algebra; Dales-Zelazko conjecture; SUBMODULES;
D O I：
10.4064/sm224-2-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Zelazko conjecture.
引用
收藏
页码：143 / 151
页数：9
相关论文
共 16 条
  • [1] [Anonymous], 1994, ENCY MATH APPL
  • [2] [Anonymous], 1993, K THEORY C ALGEBRAS, DOI DOI 10.1112/BLMS/27.2.196
  • [3] [Anonymous], 1970, J. Functional Analysis, DOI DOI 10.1016/0022-1236(70)90063-7
  • [4] Blecher D., 2004, London Math. Soc. Monogr. (N.S.), V30
  • [5] Blecher D. P., ARXIV14071356
  • [6] Blecher D. P., ARXIV14055551
  • [7] Boudi N, 2002, IRISH MATH SOC B, V48, P17
  • [8] Brown L. G., 1985, 1121185 MSRI
  • [9] Generators of maximal left ideals in Banach algebras
    Dales, H. G.
    Zelazko, W.
    [J]. STUDIA MATHEMATICA, 2012, 212 (02) : 173 - 193
  • [10] Dales H. G., 2000, London Mathematical Soci- ety Monographs New Series, V24
12