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Elements of Geometry of Balls in Banach Spaces最新文献

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Projections on balls and convex sets 球和凸集上的投影
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0006
K. Goebel, S. Prus
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引用次数: 0
Three special topics 三个专题
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0009
K. Goebel, S. Prus
{"title":"Three special topics","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0009","DOIUrl":"https://doi.org/10.1093/OSO/9780198827351.003.0009","url":null,"abstract":"First, the girth of the sphere, the infimum of length of arcs joining antipodal points on the sphere is discussed. Second, a coefficient measuring maximal separation of sequences contained in the ball is presented. Special properties of weakly convergent sequences are observed.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124657025","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
Measures of noncompactness and related properties 非紧性和相关性质的度量
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0010
K. Goebel, S. Prus
{"title":"Measures of noncompactness and related properties","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0010","DOIUrl":"https://doi.org/10.1093/OSO/9780198827351.003.0010","url":null,"abstract":"Attempts to classify properties of the ball B, or the space X, utilizing the notion of measures of noncompactness are presented. They are connected with the Kadec–Klee property. Measures of noncompactness are used to generalize the notion of uniform convexity and smoothness.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132207960","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
Low dimensional spaces 低维空间
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/oso/9780198827351.003.0002
K. Goebel, S. Prus
{"title":"Low dimensional spaces","authors":"K. Goebel, S. Prus","doi":"10.1093/oso/9780198827351.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198827351.003.0002","url":null,"abstract":"The chapter is devoted to build the reader’s geometrical intuition. It contains a list of examples of norms in low dimensional spaces. Special features of two-dimensional spaces are described in more detail.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134401633","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
More moduli and coefficients 更多的模和系数
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/oso/9780198827351.003.0007
K. Goebel, S. Prus
{"title":"More moduli and coefficients","authors":"K. Goebel, S. Prus","doi":"10.1093/oso/9780198827351.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780198827351.003.0007","url":null,"abstract":"The general construction of multi-dimensional Milman’s moduli is described. Two-dimensional moduli are related to uniform convexity and uniform smoothness. The James constant measuring nonsquareness of the ball is discussed. A universal modulus, called also the modulus of squareness, and related both to convexity and smoothness is studied.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124752570","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
Smoothness and uniform smoothness 平整度和均匀平整度
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0004
K. Goebel, S. Prus
{"title":"Smoothness and uniform smoothness","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0004","DOIUrl":"https://doi.org/10.1093/OSO/9780198827351.003.0004","url":null,"abstract":"The notions of smoothness and uniform smoothness of a space are discussed. The relation with differentiability of the norm is shown. The main tool, the modulus of smoothness of a space is studied.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123530251","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
Uniform smoothness vs uniform convexity 均匀平滑vs均匀凸性
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/oso/9780198827351.003.0005
K. Goebel, S. Prus
{"title":"Uniform smoothness vs uniform convexity","authors":"K. Goebel, S. Prus","doi":"10.1093/oso/9780198827351.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198827351.003.0005","url":null,"abstract":"The aim of the chapter is to present duality between uniform convexity and uniform smoothness. Lindenstrauss formulas relating moduli of convexity and smoothness are discussed as the main tool. A section deals with the notion of noncreasy and uniformly noncreasy spaces.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127284028","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
Strict and uniform convexity 严格一致的凸性
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0003
K. Goebel, S. Prus
{"title":"Strict and uniform convexity","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0003","DOIUrl":"https://doi.org/10.1093/OSO/9780198827351.003.0003","url":null,"abstract":"Ways to classify and measure convexity of balls are described. Properties like strict convexity, uniform convexity, and squareness are discussed. The main tool, the modulus of convexity of a space, is studied. In the case of uniformly convex spaces, nearest point projections and asymptotic centres of sequences are presented.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"284 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116162650","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
Basics and prerequisites 基础知识和先决条件
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/OSO/9780198827351.003.0001
K. Goebel, S. Prus
{"title":"Basics and prerequisites","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0001","DOIUrl":"https://doi.org/10.1093/OSO/9780198827351.003.0001","url":null,"abstract":"The chapter contains notation and an overview of prerequisites needed to understand the further text. They mostly correspond to the standard course of functional analysis. A few more advanced subjects like criteria of reflexivity, finite dimensional decompositions, etc., are briefly described.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"8 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115468194","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
Radius vs diameter 半径与直径
Elements of Geometry of Balls in Banach Spaces Pub Date : 2018-09-13 DOI: 10.1093/oso/9780198827351.003.0008
K. Goebel, S. Prus
{"title":"Radius vs diameter","authors":"K. Goebel, S. Prus","doi":"10.1093/oso/9780198827351.003.0008","DOIUrl":"https://doi.org/10.1093/oso/9780198827351.003.0008","url":null,"abstract":"The subject of the chapter is the relationship between the (Chebyshev) radius and diameter of convex bounded sets. The main tool is the Jung coefficient. Diametral sets and normal structure in connection with the fixed point theory for nonexpansive mappings are presented.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124360336","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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