Hyperinvariant Subspaces for Some 2x2 Operator Matrices
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The rst 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).
Abstract
The rst 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).
참고문헌 (8)
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- H. J. Kim, "Hyperinvariant subspaces for operators having a compact part", J. Math. Anal. Appl, 386, pp.110~114 (2012)
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