Hyperinvariant subspaces for some 2 × 2 operator matrices, II

Il Bong Jung, Eungil Ko, Carl Pearcy

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Abstract

In a previous paper, the authors of this paper studied 2×2 matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1; 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the 2×2 matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such 2 × 2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

Original languageEnglish
Pages (from-to)225-231
Number of pages7
JournalKyungpook Mathematical Journal
Volume59
Issue number2
DOIs
StatePublished - 2019

Keywords

  • Compact operator
  • Hyperinvariant subspace
  • Invariant subspace

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