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 AB(H,K)A \in \mathcal B(\mathcal H,\mathcal K), CB(H,K)C \in \mathcal B(\mathcal H,\mathcal K) does there exist operators TB(H,L)T \in \mathcal B(\mathcal H,\mathcal L) and SB(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 (2018), no. 2, pp. 635–649

DOI 10.4171/JST/258