A positive answer on Nirenberg's problem on expansive mappings in Hilbert spaces
type: Item
instance of: scholarly article
title: A positive answer on Nirenberg's problem on expansive mappings in Hilbert spaces
DOI: 10.1155/2022/9487405
author: Teffera M. Asfaw
published in: Abstract and Applied Analysis
publication date: 2022-12-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47B02
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7637323
zbMATH Keywords: expansive operator
zbMATH Keywords: Nirenberg's problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/9487405
OpenAlex ID: W4220798794
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cites work: Solution to a problem of Nirenberg concerning expanding maps
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description: scientific article; zbMATH DE number 7637323