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

Teffera M. Asfaw and Dumitru Motreanu

Abstract and Applied Analysis, 2022, vol. 2022, 1-5

Abstract: 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 RT∘≠∅. I shall give a positive answer for the problem provided that RT∘ 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:9487405

DOI: 10.1155/2022/9487405

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