反三角算子矩阵的右可逆性和谱-数学专业毕业论文.pdfVIP

反三角算子矩阵的右可逆性和谱 摘要 本文针对某类无界反三角算子矩阵^，=(。A：)，给出了其值域的稠密 性、闭性以及右可逆性可由次对角元素刻画的充分必要条件．此外，借助二次 补算子，描述了M为单射、满射和值域稠密等性质，进而刻画其点谱，连续谱 和剩余谱． 关键词：反三角算子矩阵；右可逆性；点谱；连续谱；剩余谱 2013JQ01)资助 万方数据 THERIGHT INVERTIBILITYANDSPECTRUMoF ANTI-TRIANGULARoPERAToRMA，I’RICES ABSTRACT For aclassof matrices densenessandthe anti—triangularoperator M=(务0)，the closednessoftheir andthe are somesufficientand range rightinvertibilitystudied，and conditionsfor necessary themtobecharacterized entriesare by off-diagonal given．Be- of sides，thespectrum matrices studied．The anti—triangularoperator M=(参o)is and of properties，includinginjectiveness，surjectiveness densityrange，arepresentedby the the quadratic andresidual complements，andpointspectrum，continuous spectrum are thendescribed． spectrum KEYWORDS：anti—triangularoperatormatrix；right invertibility；pointspectrum；con— tinuous spectrum；residual spectrum Thisworkis theNNSFof 1461049and1 supportedby 1371 theNSFofInner China(Nos．1 185)and Mongolia(No．2013Jq01)． 11 万方数据 目 录 中文摘要 英文摘要 主要符号表 第一章 绪论