A note on the orthogonality equation with two functions

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• 作者：Radosław Łukasik
• 关键词：Orthogonality equation ; Hilbert space ; adjoint operator
• 刊名：Aequationes Mathematicae
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：90
• 期：5
• 页码：961-965
• 全文大小：394 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903
• 卷排序：90

文摘

The aim of this paper is to describe the solution (f, g) of the equation$$\langle{f(x)}|{g(y)}\rangle=\langle{x}|{y}\rangle,\quad x,y\in D,$$where \({f,g\colon D\to Y}\), X, Y are Hilbert spaces over the same field \({\mathbb{K} \in \{\mathbb{R}, \mathbb{C}\}}\), D is a dense subspace of X.KeywordsOrthogonality equationHilbert spaceadjoint operatorMathematics Subject ClassificationPrimary 39B5247A05Secondary 47A62Download to read the full article textReferences1.Akhiezer N.I., Glazman I.M.: Theory of Linear Operators in Hilbert Space. Dover Publications Inc., New York (1993)MATHGoogle Scholar2.Chmieliński, J.: Orthogonality equation with two unknown functions. Aequ. Math. doi:10.1007/s00010-015-0359-x 3.Chmieliński, J., Łukasik R., Wójcik P.: On the stability of the orthogonality equation and orthogonality preserving property with two unknown functions. Banach J. Math. Anal. (accepted)4.Łukasik, R., Wójcik, P.: Decomposition of two functions in the orthogonality equation. Aequ. Math. doi:10.1007/s00010-015-0385-8 Copyright information© The Author(s) 2016Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.