A Positive Answer on Nirenberg's Problem on Expansive Mappings in Hilbert Spaces.

Nirenberg proposed a problem as to whether or not a continuous and expansive operator T : X ⟶ X (where X is a Hilbert space) is surjective if R T ∘ ≠ ∅. I shall give a positive answer for the problem provided that R T ∘ is unbounded. For contents related to this paper, the reader is referred to the remarks and the study of Asfaw (2021). The present paper gives a complete answer for the problem that has been open for about 47 years. [ABSTRACT FROM AUTHOR]