Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
基本信息
- 批准号:238949-2011
- 负责人:
- 金额:$ 0.73万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2015
- 资助国家:加拿大
- 起止时间:2015-01-01 至 2016-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Since M. Gelfand's pioneer work on normed rings was published in 1941, Banach algebra theory has become a major field in functional analysis. The theory, standing between analysis and algebra in its nature, has had a deep influence upon modern mathematics. The proposed research will focus on topological and algebraic structures of Banach algebras, their second duals and their ideals. We will also investigate the amenability properties and fixed point properties of semigroups. The study of cohomology in Banach algebras began in 1970s. Results achieved on this subject often represent significant progress in the development of Banach algebra theory. Cohomology studies the difference, in terms of cohomology groups, of the spaces of coboundaries and cocycles. In tradition, coboundaries and cocycles are treated as just linear spaces, and hence a cohomology group is simply an algebraic object. However, these spaces may be naturally equipped with various topologies. One can consider "topological" cohomology for Banach algebras. This is the direction in which I will explore for the program. The recently introduced various types of generalized amenability for Banach algebras may be interpreted as "topological triviality" of the first cohomology group with respect to specific topologies. There are many open problems regarding generalized amenability. I will target them. Arens products on the second dual of a Banach algebra are significant objects in Banach algebras. Arens regularity, topological centers and multipliers will be investigated for important Banach algebras. Counterparts in Banach algebras of crucial objects/notions in harmonic analysis will be investigated. Various types of approximate identities for ideals will also be studied. Amenability properties of a semigroup S, such as invariant means on WAP(S), LUC(S) and C(S), will be studied in the program. There are deep relations between amenability properties and fixed point properties for a semitopological semigroup. I will study these relations. Semigroups of non-expansive self mappings on a closed subset of a Banach space will be particularly concerned. Fixed point property of this type of mappings is extremely important in the field of nonlinear analysis.
自从M. Gelfand的先驱工作,赋范环发表于1941年,Banach代数理论已成为一个主要领域的功能分析。该理论,站在分析和代数之间的性质,对现代数学产生了深刻的影响。本论文的主要研究内容是Banach代数的拓扑结构、代数结构、第二类Banach代数及其理想。我们还将研究半群的顺从性和不动点性质。Banach代数上同调的研究始于20世纪70年代。在这一问题上取得的成果往往代表着Banach代数理论发展的重大进展。上同调研究上边界空间和上循环空间在上同调群方面的差异。在传统上,上边界和上圈被视为线性空间,因此上同调群只是一个代数对象。然而,这些空间可以自然地配备有各种拓扑结构。可以考虑Banach代数的“拓扑”上同调。这是我将为该计划探索的方向。最近提出的Banach代数的各种类型的广义顺从性可以解释为第一上同调群关于特定拓扑的“拓扑平凡性”。关于广义顺从性,有许多悬而未决的问题。我会瞄准他们。Banach代数的第二对偶上的Arens积是Banach代数中的重要对象。阿伦斯正则性,拓扑中心和乘子将被调查的重要Banach代数。将研究调和分析中关键对象/概念在Banach代数中的对应物。各种类型的近似身份的理想也将研究。该程序将研究半群S的顺从性,如WAP(S),LUC(S)和C(S)上的不变平均。 拓扑半群的顺从性与不动点性质之间有着深刻的联系。我将研究这些关系。Banach空间的闭子集上的非扩张自映射半群将特别受到关注。这类映射的不动点性质在非线性分析领域中是极其重要的。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Zhang, Yong其他文献
Atmospheric observations suggest methane emissions in north-eastern China growing with natural gas use.
- DOI:
10.1038/s41598-022-19462-4 - 发表时间:
2022-11-17 - 期刊:
- 影响因子:4.6
- 作者:
Wang, Fenjuan;Maksyutov, Shamil;Janardanan, Rajesh;Tsuruta, Aki;Ito, Akihiko;Morino, Isamu;Yoshida, Yukio;Tohjima, Yasunori;Kaiser, Johannes W.;Lan, Xin;Zhang, Yong;Mammarella, Ivan;Lavric, Jost, V;Matsunaga, Tsuneo - 通讯作者:
Matsunaga, Tsuneo
Exploring the Action Mechanism of the Active Ingredient of Quercetin in Ligustrum lucidum on the Mouse Mastitis Model Based on Network Pharmacology and Molecular Biology Validation.
- DOI:
10.1155/2022/4236222 - 发表时间:
2022 - 期刊:
- 影响因子:0
- 作者:
Cao, Lu;Wang, Tao;Mi, XiaoYu;Ji, Peng;Zhao, XingXu;Zhang, Yong - 通讯作者:
Zhang, Yong
Fluorescence-guided surgery improves outcome in an orthotopic osteosarcoma nude-mouse model.
- DOI:
10.1002/jor.22706 - 发表时间:
2014-12 - 期刊:
- 影响因子:2.8
- 作者:
Miwa, Shinji;Hiroshima, Yukihiko;Yano, Shuya;Zhang, Yong;Matsumoto, Yasunori;Uehara, Fuminari;Yamamoto, Mako;Kimura, Hiroaki;Hayashi, Katsuhiro;Bouvet, Michael;Tsuchiya, Hiroyuki;Hoffman, Robert M. - 通讯作者:
Hoffman, Robert M.
Altered static and dynamic functional connectivity of habenula in first-episode, drug-naïve schizophrenia patients, and their association with symptoms including hallucination and anxiety.
- DOI:
10.3389/fpsyt.2023.1078779 - 发表时间:
2023 - 期刊:
- 影响因子:4.7
- 作者:
Xue, Kangkang;Chen, Jingli;Wei, Yarui;Chen, Yuan;Han, Shaoqiang;Wang, Caihong;Zhang, Yong;Song, Xueqin;Cheng, Jingliang - 通讯作者:
Cheng, Jingliang
Bayesian Analysis of Climate Change Effects on Observed and Projected Airborne Levels of Birch Pollen.
- DOI:
10.1016/j.atmosenv.2012.11.028 - 发表时间:
2013-04-01 - 期刊:
- 影响因子:5
- 作者:
Zhang, Yong;Isukapalli, Sastry S.;Bielory, Leonard;Georgopoulos, Panos G. - 通讯作者:
Georgopoulos, Panos G.
Zhang, Yong的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Zhang, Yong', 18)}}的其他基金
Amenability properties of semitopological semigroups and related Banach algebras
半拓扑半群和相关巴纳赫代数的顺应性性质
- 批准号:
RGPIN-2022-04137 - 财政年份:2022
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2021
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2020
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2019
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2018
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2017
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Amenability properties and related problems of Banach algebras associated to groups and semigroups
与群和半群相关的 Banach 代数的顺应性性质和相关问题
- 批准号:
RGPIN-2016-05987 - 财政年份:2016
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
- 批准号:
238949-2011 - 财政年份:2014
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
- 批准号:
238949-2011 - 财政年份:2013
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
- 批准号:
238949-2011 - 财政年份:2012
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
Banach空间上多变量算子的若干问题
- 批准号:12371139
- 批准年份:2023
- 资助金额:44.00 万元
- 项目类别:面上项目
Banach空间非线性粗等距的稳定性及其应用
- 批准号:12301163
- 批准年份:2023
- 资助金额:30 万元
- 项目类别:青年科学基金项目
相关于球拟Banach函数空间的Besov空间和Triebel-Lizorkin空间的实变理论及其应用
- 批准号:12301112
- 批准年份:2023
- 资助金额:30 万元
- 项目类别:青年科学基金项目
Banach空间非线性等距理论的研究
- 批准号:n/a
- 批准年份:2023
- 资助金额:0.0 万元
- 项目类别:省市级项目
交换子在球Banach函数空间上的有界性和紧性特征
- 批准号:12301123
- 批准年份:2023
- 资助金额:30.00 万元
- 项目类别:青年科学基金项目
泛函不等式及其在Banach空间理论与非交换分析中的应用
- 批准号:2023JJ40696
- 批准年份:2023
- 资助金额:0.0 万元
- 项目类别:省市级项目
Banach空间上非交换的非线性算子拓扑半群的遍历理论及其应用
- 批准号:12371140
- 批准年份:2023
- 资助金额:43.5 万元
- 项目类别:面上项目
Banach空间中关于变分不等式问题的外梯度迭代算法研究
- 批准号:12301159
- 批准年份:2023
- 资助金额:30 万元
- 项目类别:青年科学基金项目
有逼近性质或(余)型的Banach上的扩张问题的研究
- 批准号:12301162
- 批准年份:2023
- 资助金额:30.00 万元
- 项目类别:青年科学基金项目
Banach空间几何理论在凸微分分析和广义逆上的应用
- 批准号:12271121
- 批准年份:2022
- 资助金额:47 万元
- 项目类别:面上项目
相似海外基金
Cyclic and simplicial cohomology of Banach algebras
Banach 代数的循环和单纯上同调
- 批准号:
184058-2012 - 财政年份:2016
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
"Derivations, cohomology groups and second duals of Banach algebras"
“Banach 代数的导数、上同调群和第二对偶”
- 批准号:
36640-2012 - 财政年份:2016
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cyclic and simplicial cohomology of Banach algebras
Banach 代数的循环和单纯上同调
- 批准号:
184058-2012 - 财政年份:2015
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
"Derivations, cohomology groups and second duals of Banach algebras"
“Banach 代数的导数、上同调群和第二对偶”
- 批准号:
36640-2012 - 财政年份:2015
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cyclic and simplicial cohomology of Banach algebras
Banach 代数的循环和单纯上同调
- 批准号:
184058-2012 - 财政年份:2014
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
- 批准号:
238949-2011 - 财政年份:2014
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
"Derivations, cohomology groups and second duals of Banach algebras"
“Banach 代数的导数、上同调群和第二对偶”
- 批准号:
36640-2012 - 财政年份:2014
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cohomology in Banach algebras and amenability properties of semigroups
Banach代数中的上同调和半群的顺从性
- 批准号:
238949-2011 - 财政年份:2013
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
"Derivations, cohomology groups and second duals of Banach algebras"
“Banach 代数的导数、上同调群和第二对偶”
- 批准号:
36640-2012 - 财政年份:2013
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Cyclic and simplicial cohomology of Banach algebras
Banach 代数的循环和单纯上同调
- 批准号:
184058-2012 - 财政年份:2013
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual