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 language | English |
---|---|
Pages (from-to) | 225-231 |
Number of pages | 7 |
Journal | Kyungpook Mathematical Journal |
Volume | 59 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Publisher Copyright:© Kyungpook Mathematical Journal.
Keywords
- Compact operator
- Hyperinvariant subspace
- Invariant subspace