# Hyperinvariant Subspaces for Some 2×2 Operator Matrices

• Jung, Il Bong (Department of Mathematics, Kyungpook National University) ;
• Ko, Eungil (Department of Mathematics, Ewha Womans University) ;
• Pearcy, Carl (Department of Mathematics, Texas A&M University, College Station)
• Accepted : 2018.02.20
• Published : 2018.09.23
• 229 9

#### 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 $2{\times}2$ operator matrices (Theorem 3.2).

#### Keywords

invariant subspace;hyperinvariant subspace;extremal vector;transitive algebra

#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

#### References

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