On surjectivity and denseness of range of the operator A+CXA+CX

  • Dragana S. Cvetković-Ilić

    University of Niš, Serbia
  • Vladimir Pavlović

    University of Niš, Serbia
On surjectivity and denseness of range of the operator $A+CX$ cover
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Abstract

Motivated by a result of Takahashi from Invertible completions of operator matrices, Integr. Equ. Oper. Theory 21 (1995) 355–361, in this paper we investigate the problems of characterization of all the pairs of operators AB(H,K)A\in\mathcal B(\mathcal H,\mathcal K) and CB(L,K)C\in\mathcal B(\mathcal L,\mathcal K) for which there exists some XB(H,L)X\in\mathcal B(\mathcal H,\mathcal L) such that the operator A+CXA+CX is surjective/with dense range, for some XB(H,K)X\in\mathcal B(\mathcal H,\mathcal K). We completely solve the former and give some partial results regarding the latter one.

Cite this article

Dragana S. Cvetković-Ilić, Vladimir Pavlović, On surjectivity and denseness of range of the operator A+CXA+CX. J. Spectr. Theory 8 (2018), no. 3, pp. 871–881

DOI 10.4171/JST/215