有哪些信誉好的足球投注网站- 1、本文档共17页，可阅读全部内容。
- 2、有哪些信誉好的足球投注网站（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。
- 3、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。
查看更多
Characterizations of essential ideals as operator modules over C-algebras
a
r
X
i
v
:
m
a
t
h
/
0
1
0
2
1
3
4
v
1
[
m
a
t
h
.O
A
]
1
6
F
e
b
2
0
0
1
CHARACTERIZATIONS OF ESSENTIAL IDEALS AS OPERATOR
MODULES OVER C*-ALGEBRAS
MASAYOSHI KANEDA* AND VERN IVAL PAULSEN*
Abstract. In this paper we give characterizations of essential left ideals of a C*-algebra
A in terms of their properties as operator A-modules. Conversely, we seek C*-algebraic
characterizations of those ideals J in A such that A is an essential extension of J in various
categories of operator modules. In the case of two-sided ideals, we prove that all the above
concepts coincide. We obtain results, analogous to M. Hamana’s results, which characterize
the injective envelope of a C*-algebra as a maximal essential extension of the C*-algebra,
but with completely positive maps replaced by completely bounded module maps. By
restricting to one-sided ideals, module actions reveal clear differences which do not show up
in the two-sided case. Throughout this paper, module actions are crucial.
Date: April 25, 2000.
AMS 2000 subject classifications: Primary 46H10, 46H25, 46L07; Secondary 46A22, 46L05, 46L08, 46M10,
47D15, 47L25.
Key Words: essential ideals; left ideals; C*-module extensions.
* Supported by a grant from the NSF.
1
2 MASAYOSHI KANEDA* AND VERN IVAL PAULSEN*
1. Introduction.
Let A denote a C*-algebra. In the C*-algebra literature a two-sided ideal, J , of A is called
essential if aJ = {0} implies a = 0. Given a category and an object X contained in an
object Y, then Y is called an essential extension of X provided that every morphism of Y
that restricts to be an isomorphism of X must necessarily be an isomorphism of Y. In this
paper we study the relationships between these two different approaches to essentiality as
we vary the category.
Every left ideal can be regarded as an object in the category of operator left A-modules,
with morphisms either the completely contractive or completely bounded left A-module
maps. Thus, it is interesting to know the relationships b
您可能关注的文档
- characteristics of stemflow for tall stewartia growing on a hillslope.pdf
- Characteristics and sources of chromophoric dissolved organic matter in lakes of the Yungui Plateau.pdf
- Characterization of Electrochemically Grown Crystalline CuInSe2 Thin Films.pdf
- Characterization of PM2.5 in the ambientair of Shanghaicity by analyzingindividualparticles.pdf
- Characterizing packet audio streams from internet multimedia applications.pdf
- Charge amplification concepts for direction-sensitive dark matter detectors.pdf
- Charge carriers of different origin in cuprates as revealed by experiment.pdf
- Charge collective modes in an incommensurately modulated cuprate.pdf
- Charge exchange for medium energy He and Ne ions in a large-angle collision at solid surfaces.pdf
- Charge transport along the c-axis in high-T_c cuprates.pdf
文档评论（0）