2 × 2算子矩阵的超不变子空间

IF 0.6 Q3 MATHEMATICS

Kyungpook Mathematical Journal Pub Date : 2020-01-01 DOI:10.5666/KMJ.2019.59.2.225

I. Jung, E. Ko, C. Pearcy

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引用次数: 4

摘要

在上篇文章中，作者研究了上三角形式的2x2矩阵，其元素是Hilbert空间上的算子，其中(1,1)元素有一个非平凡的超不变子空间。我们能够证明，在某些情况下，2x2矩阵本身有一个非平凡的超不变子空间。它推广了h.j. Kim在2011年和2012年提出的两个很好的定理，并在解决一个已经开放了45年的问题方面取得了一些进展。在本文中，我们继续研究这样的2 × 2算子矩阵，我们改进了我们以前的结果，也许使我们更接近于解决长期存在的开放问题，如上所述。

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Hyperinvariant subspaces for some 2 × 2 operator matrices, II

In a previous paper, the authors of this paper studied 2× 2 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 2× 2 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 our investigation of such 2 × 2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

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来源期刊

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.