JournalsjstVol. 7, No. 4pp. 1023–1038

Fredholm consistency of upper-triangular operator matrices

  • Dragana S. Cvetković-Ilić

    University of Niš, Serbia
Fredholm consistency of  upper-triangular operator matrices cover
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Abstract

In this paper, for given operators AB(H)A\in\mathcal B(\mathcal H) and BB(K)B\in\mathcal B(\mathcal K), we characterize the set of all CB(K,H)C\in\mathcal B(\mathcal K,\mathcal H) such that the operator matrix MC=[AC0B]M_C= \left[ {\begin{array}{cc} A & C \\ 0 & B \\ \end{array} } \right] is Fredholm consistent. We completely describe the sets CB(K,H)σFC(MC)\bigcap_{C\in \mathcal B(\mathcal K,\mathcal H)}\sigma_{\mathrm{FC}}(M_C) and CB(K,H)σFC(MC)\bigcup_{C\in \mathcal B(\mathcal K,\mathcal H)}\sigma_{\mathrm{FC}}(M_C). Also, we prove that CB(K,H)σFC(MC)=σFC(M0)\bigcap_{C\in \mathcal B(\mathcal K,\mathcal H)}\sigma_{\mathrm{FC}}(M_C)=\sigma_{\mathrm{FC}}(M_0).

Cite this article

Dragana S. Cvetković-Ilić, Fredholm consistency of upper-triangular operator matrices. J. Spectr. Theory 7 (2017), no. 4, pp. 1023–1038

DOI 10.4171/JST/184