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Introductory Theory of Topological Vector Spaces最新文献

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Dual Pairs and the Weak Topology 双对与弱拓扑
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-16
Yau-chuen Wong
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引用次数: 0
A Structure Theorem for Compact Sets in a Banach Space Banach空间中紧集的结构定理
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-5
Yau-chuen Wong
{"title":"A Structure Theorem for Compact Sets in a Banach Space","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-5","DOIUrl":"https://doi.org/10.1201/9780203749807-5","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123367434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normed Spaces Associated with a Locally Convex Space 与局部凸空间相关的赋范空间
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-10
Yau-chuen Wong
{"title":"Normed Spaces Associated with a Locally Convex Space","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-10","DOIUrl":"https://doi.org/10.1201/9780203749807-10","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123367649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Projective Topologies and Inductive Topologies 射影拓扑与归纳拓扑
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-9
Yau-chuen Wong
{"title":"Projective Topologies and Inductive Topologies","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-9","DOIUrl":"https://doi.org/10.1201/9780203749807-9","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126250208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Banach Spaces and Hilbert Spaces 巴拿赫空间和希尔伯特空间
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-2
Yau-Chuen Wong
{"title":"Banach Spaces and Hilbert Spaces","authors":"Yau-Chuen Wong","doi":"10.1201/9780203749807-2","DOIUrl":"https://doi.org/10.1201/9780203749807-2","url":null,"abstract":"Recall the definitions of a norm and inner product on a real vector space V. We will assume a basic knowledge of these concepts, as can be found in any linear algebra book. The following proposition defines a metric topology on any normed vector space: Then d is a metric on V , and the norm · is continuous in the metric topology. PROOF The axioms for a metric are easy to check — the triangle inequality follows from the triangle inequality for norms. The continuity of the norm follows from the continuity of d and the fact that v = d(v, 0). Definition: Banach Spaces A Banach space is a normed vector space whose associated metric is complete. For example, any norm on a finite-dimensional vector space is complete, and therefore any finite-dimensional normed vector space is a Banach space. However, the term \" Banach space \" is mostly used only in the context of infinite-dimensional spaces. We begin by giving some basic examples of infinite-dimensional Banach spaces.","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127669115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operators and Some Consequences of Hahn-Banach’s Extension Theorem 哈恩-巴拿赫扩展定理的算子和一些结果
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-3
Yau-chuen Wong
{"title":"Operators and Some Consequences of Hahn-Banach’s Extension Theorem","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-3","DOIUrl":"https://doi.org/10.1201/9780203749807-3","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132819994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Precompact Seminorms and Schwartz Spaces 预紧半实与Schwartz空间
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-20
Yau-chuen Wong
{"title":"Precompact Seminorms and Schwartz Spaces","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-20","DOIUrl":"https://doi.org/10.1201/9780203749807-20","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130780448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Initial Bornologies and Final Bornologies 初始龙骨学和最终龙骨学
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-14
Yau-chuen Wong
{"title":"Initial Bornologies and Final Bornologies","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-14","DOIUrl":"https://doi.org/10.1201/9780203749807-14","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127915356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Recent Results on Compact Operators and Weakly Compact Operators 紧算子和弱紧算子的一些最新结果
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-19
Yau-chuen Wong
{"title":"Some Recent Results on Compact Operators and Weakly Compact Operators","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-19","DOIUrl":"https://doi.org/10.1201/9780203749807-19","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115913508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elementary Duality Theory 初等对偶理论
Introductory Theory of Topological Vector Spaces Pub Date : 2019-01-25 DOI: 10.1201/9780203749807-17
Yau-chuen Wong
{"title":"Elementary Duality Theory","authors":"Yau-chuen Wong","doi":"10.1201/9780203749807-17","DOIUrl":"https://doi.org/10.1201/9780203749807-17","url":null,"abstract":"","PeriodicalId":218491,"journal":{"name":"Introductory Theory of Topological Vector Spaces","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114769796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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