Hyperinvariant Subspaces for Some 2x2 Operator Matrices, II
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In a previous paper, the authors of this paper studied 2x2 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 2x2 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 ourinvestigation of such 2x2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.
Abstract
In a previous paper, the authors of this paper studied 2x2 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 2x2 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 ourinvestigation of such 2x2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.
참고문헌 (10)
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