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关于广义Aluthge变换的数值域的研究 被引量：1

On the Numerical Range of the Generalized Aluthge Transforms
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摘要 设T∈B(H),T=U|T|是算子T的极分解,则定义Tt=|T|tU|T|1-t和Tt(*)=|T*|tU|T*|1-t(其中0<t<1)分别为算子的广义Aluthge变换和广义*-Aluthge变换。文章主要利用算子矩阵分块技巧,研究了三者之间的本性谱、数值域、本性数值域的关系,推广了吴培元的结果。 LetT∈B（H）,T=UITI is a polar decomposition ofT,then defined. T^～1=｜T｜^1U｜T｜^1-i and T^～（＊）=｜T^＊｜^U｜T＊｜^1-i to be the generalized Aluthge transform and the genralized - Aluthge transform of T respectively, νt∈ （0,1）. Wo discuss mainly on the relationships among them, including the essential spectrum, numerical ruage and the essential numerical range.
作者 陈冬君 张云
机构地区 淮北煤炭师范学院数学系
出处 《云南师范大学学报（自然科学版）》 2008年第3期21-26,共6页 Journal of Yunnan Normal University:Natural Sciences Edition
基金 安徽省高校省级自然科学研究重点项目基金资助(2006Kj09A)
关键词 广义ALUTHGE变换 广义＊-Aluthge变换 数值域 本性数值域 the generalized Aluthge transform the genralized ＊-Aluthge transform numerical rnage essential numrical range
分类号 O177.1 [理学—基础数学]
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参考文献13

  • 1Wu, P, Y. Numerical range of the Aluthge transform of operator, Linear Alg. App1,2002,357,295 -298.
  • 2Jung,I. B. ,Ko ,E. and Pearcy. C. Muthge transforms of operators. Integral Equations and Operator Theory ,2000,37,437 -448.
  • 3Jung, I. B. , Ko, E. and Pearcy. C. Spectral picture of Aluthge transforms of operators. Inte - gral Equations and Operator Theory, 2001,40,52 - 60.
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同被引文献9

  • 1ALUTHGE A. On p-hypononnal operators for 0< p < 1[J]. Integral Equations and Operator Theory, 1990, 13:307-315.
  • 2YAMAZAKI T. Parallelisms between Alufllge transformation and powers of operators[J]. Acta Sci Math: Szeged, 2001, 67:809-820.
  • 3JUNG I B, KO E, PEARCY C. Aluthge transforms of operators[J]. Integral Equations and Operator Theory, 2000, 37:437-448.
  • 4JUNG I B, KO E, PEARCY C. Spectral picture of Aluthge transforms of operators[J]. Integral Equations and Operator Theory, 2001, 40:52-60.
  • 5YAMAZAKI T. On numerical range of the Aluthge transformation[ J]. Linear Alg Appl, 2002, 341:111-117.
  • 6JI Guoxing, LIU Ni, LI Ze. Essential numerical range and maximal numerical range of the Aluthge transform[J]. Linear and Multilinear Algebra, 2007, 55(4) :315-322.
  • 7BROWN L J, DOUGLAS R G, FILLMORE P A. Unitary equivalence modulo the compact operators and extensions of C^* algebras[ C]// Proceeding of a Conference on Operator Theory, Lecture Notes in Mathemat. Heidelberg: Springer-Verlag, 1973, 345:58-128.
  • 8MURPHY G J. C^* -algebras and operator theory[M]. London: Academic press, 1990.
  • 9张云,吉国兴.关于广义Aluthge变换的谱性质的研究(英文)[J].应用泛函分析学报,2008,10(2):116-122. 被引量：4

引证文献1

云南师范大学学报（自然科学版）
2008年 第3期

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