On the Invariant Subspace Problem

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• 作者：M. Sababheh ; A. Yousef…
• 关键词：Invariant subspace ; Operator on Hilbert spaces
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：39
• 期：2
• 页码：699-705
• 全文大小：390 KB
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  3.Chalendar, I., Partington, J.R.: An overview of some recent developments on the invariant subspace problem. Concr. Oper. 1, 1–10 (2012)CrossRef MATH
  4.Enflo, P.: On the invariant subspace problem for Banach spaces. Acta Math. 158, 213–313 (1987)MathSciNet CrossRef MATH
  5.Lomonosov, V.I.: Invariant subspaces of the family of operators that commute with a completely continuous operator. Funkc. Anal. i Pril. 7(3), 55–56 (1973)MathSciNet
  6.Read, C.J.: A solution to the invariant subspace problem on the space \(\ell ^1\) . Bull. Lond. Math. Soc. 17, 305–317 (1985)MathSciNet CrossRef MATH
  7.Yadav, B.S.: The present state and heritages of the invariant subspace problem. Milan J. Math. 73, 289–316 (2005)MathSciNet CrossRef MATH
  
• 作者单位：M. Sababheh (1)
  A. Yousef (2)
  R. Khalil (2)
  
  1. Department of Basic Sciences, Princess Sumaya University For Technology, Al Jubaiha, Amman, 11941, Jordan
  2. Department of Mathematics, The University of Jordan, Al Jubaiha, Amman, 11942, Jordan
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

In an attempt to solve the invariant subspace problem, we introduce a certain orthonormal basis of Hilbert spaces, and prove that a bounded linear operator on a Hilbert space must have an invariant subspace once this basis fulfills certain conditions. Ultimately, this basis is used to show that every bounded linear operator on a Hilbert space is the sum of a shift and an upper triangular operators, each of which having an invariant subspace.