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

Q3 Mathematics Abstract and Applied Analysis Pub Date : 2022-03-17 DOI:10.1155/2022/9487405

Teffera M. Asfaw

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引用次数: 2

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

\overset{\circ}{R (T)} \neq \emptyset

. I shall give a positive answer for the problem provided that

\overset{\circ}{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.

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Hilbert空间中扩展映射的Nirenberg问题的一个肯定答案

Nirenberg提出了一个问题，即是否存在一个连续的可拓算子T:X⟶ X（其中X是希尔伯特空间）是满射的，如果R T∘≠∅。如果R T∘是无界的。关于本文的相关内容，读者可参考Asfaw（2021）的评论和研究。本文对这个开放了大约47年的问题给出了一个完整的答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.