A positive answer on Nirenberg's problem on expansive mappings in Hilbert spaces
Summary: Nirenberg [1] proposed a problem as to whether or not a continuous and expansive operator \(T:X\rightarrowX \) (where \(X\) is a Hilbert space) is surjective if \(\mathring{R \left( T\right)}\neq\varnothing \). I~shall give a positive answer for the problem provided that \(\mathring{R \left( T\right)}\) is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of the author [\textit{T. M. Asfaw}, J. Math. Anal. Appl. 493, No. 1, Article ID 124526, 10 p. (2021; Zbl 1457.46074)]. The present paper gives a complete answer for the problem that has been open for about 47 years.
scientific article; zbMATH DE number 7637323
scientific article