Hyperinvariant subspaces for some 2×2 operator matrices

Il Bong Jung, Eungil Ko, Carl Pearcy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of 2 × 2 operator matrices (Theorem 3.2).

Original languageEnglish
Pages (from-to)489-494
Number of pages6
JournalKyungpook Mathematical Journal
Volume58
Issue number3
DOIs
StatePublished - 2018

Bibliographical note

Funding Information:
Acknowledgement. The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2015R1A2A2A01006072). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937).

Funding Information:
The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2015R1A2A2A01006072). The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937).

Publisher Copyright:
© Kyungpook Mathematical Journal.

Keywords

  • Extremal vector
  • Hyperinvariant subspace
  • Invariant subspace
  • Transitive algebra

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