Articles
Kyungpook Mathematical Journal 2018; 58(3): 489-494
Published online September 30, 2018
Copyright © Kyungpook Mathematical Journal.
Hyperinvariant Subspaces for Some 2×2 Operator Matrices
Il Bong Jung*
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
e-mail : ibjung@knu.ac.kr
Eungil Ko
Department of Mathematics, Ewha Womans University, Seoul 03760, Korea
e-mail : eiko@ewha.ac.kr
Carl Pearcy
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
e-mail : cpearcy@math.tamu.edu
Received: December 26, 2017; Accepted: February 20, 2018
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).
Keywords: invariant subspace, hyperinvariant subspace, extremal vector, transitive algebra.