{"title":"线性关系及其奇异链","authors":"T. Berger, H. Snoo, C. Trunk, H. Winkler","doi":"10.31392/mfat-npu26_4.2021.01","DOIUrl":null,"url":null,"abstract":"Abstract. Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for not necessarily finite-dimensional linear spaces. This leads to an identity characterizing a singular chain space in terms of root spaces. The so-called proper eigenvalues of a linear relation play an important role in the finite-dimensional case.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Linear relations and their singular chains\",\"authors\":\"T. Berger, H. Snoo, C. Trunk, H. Winkler\",\"doi\":\"10.31392/mfat-npu26_4.2021.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for not necessarily finite-dimensional linear spaces. This leads to an identity characterizing a singular chain space in terms of root spaces. The so-called proper eigenvalues of a linear relation play an important role in the finite-dimensional case.\",\"PeriodicalId\":44325,\"journal\":{\"name\":\"Methods of Functional Analysis and Topology\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2020-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods of Functional Analysis and Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31392/mfat-npu26_4.2021.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods of Functional Analysis and Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31392/mfat-npu26_4.2021.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract. Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for not necessarily finite-dimensional linear spaces. This leads to an identity characterizing a singular chain space in terms of root spaces. The so-called proper eigenvalues of a linear relation play an important role in the finite-dimensional case.
期刊介绍：
Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.
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