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

Dragana S. Cvetković-Ilić; Vladimir Pavlović

doi:10.4171/jst/215

JournalsjstVol. 8, No. 3pp. 871–881

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

Dragana S. Cvetković-Ilić
University of Niš, Serbia
Vladimir Pavlović
University of Niš, Serbia

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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 $A \in B (H, K)$ and $C \in B (L, K)$ for which there exists some $X \in B (H, L)$ such that the operator $A + CX$ is surjective/with dense range, for some $X \in B (H, K)$ . 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 $A + CX$ . J. Spectr. Theory 8 (2018), no. 3, pp. 871–881

DOI 10.4171/JST/215