On subscalarity of some 2 × 2 class A operator matrices

Eungil Ko, Sungeun Jung, Yoenha Kim

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4 Scopus citations


In this paper we provide some conditions for 2×2 operator matrices whose diagonal entries are class A operators to be subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. In addition, we show that the tensor product of a 2×2 upper triangular class A operator matrix and a class A operator has a scalar extension. Finally, we find some subscalar 2×2 operator matrices satisfying the operator equations ABA=A2 and BAB=B2.

Original languageEnglish
Pages (from-to)1322-1338
Number of pages17
JournalLinear Algebra and Its Applications
Issue number3
StatePublished - 1 Feb 2013

Bibliographical note

Funding Information:
This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012-0006691). The second author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [NRF-2011-355-1-C00005]. E-mail addresses: ssung105@ewhain.net (S. Jung), yoenha@ewhain.net (Y. Kim), eiko@ewha.ac.kr (E. Ko).


  • Class A operator
  • Invariant subspace
  • Subscalar


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