JournalsjstVol. 9, No. 2pp. 635–649

Consistency in invertibility and Fredholmness of operator matrices

  • Dragana S. Cvetković-Ilić

    University of Niš, Serbia

  • Marko Kostadinov

    University of Niš, Serbia
Consistency in invertibility and Fredholmness of operator matrices cover
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Abstract

In this paper we completely answer the following question: for given A∈B(H,K)A \in \mathcal B(\mathcal H,\mathcal K), C∈B(H,K)C \in \mathcal B(\mathcal H,\mathcal K) does there exist operators T∈B(H,L)T \in \mathcal B(\mathcal H,\mathcal L) and S∈B(K)S \in \mathcal B(\mathcal K) such that the operator

[ACTS]\left[ {\begin{array}{cc} A & C \\ T & S \\ \end{array} } \right]

is consistent in invertibility and Fredholmness?

Cite this article

Dragana S. Cvetković-Ilić, Marko Kostadinov, Consistency in invertibility and Fredholmness of operator matrices. J. Spectr. Theory 9 (2019), no. 2, pp. 635–649

DOI 10.4171/JST/258