Isosceles-orthogonality preserving property and its stability

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• 作者：Jacek Chmieliń ; ski ; Paweł ; Wó ; jcik
• 关键词：Isosceles-orthogonality ; Approximate orthogonality ; Orthogonality preserving mappings ; Linear preservers ; Stability
• 刊名：Nonlinear Analysis
• 出版年：2010
• 出版时间：1 February 2010
• 年：2010
• 卷：72
• 期：3-4
• 页码：1445-1453
• 全文大小：513 K

文摘

For real normed spaces, we consider the class of linear operators, preserving approximately the relation of isosceles-orthogonality. We show some general properties of such mappings. Next, we examine whether an approximately orthogonality preserving mapping admits an approximation by an orthogonality preserving one. In regard to this, we generalize some results obtained earlier for inner product spaces with standard orthogonality relation.