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

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  • Teffera M. Asfaw

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.

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Handle: RePEc:wly:jnlaaa:v:2022:y:2022:i:1:n:9487405
DOI: 10.1155/2022/9487405
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