Mappings approximately preserving orthogonality in normed spaces

作者：Mojskerc Blaz; Turnsek Aleksej^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(12): 3821-3831.

DOI：10.1016/j.na.2010.08.007

• Birkhoff-James orthogonality
• Approximate orthogonality
• Orthogonality preserving mapping
• Stability
• Isometry

We answer many open questions regarding approximately orthogonality preserving mappings (in Birkhoff-James sense) in normed spaces. In particular, we show that every approximately orthogonality preserving linear mapping (in Chmielinski sense) is necessarily a scalar multiple of an epsilon-isometry. Thus, whenever epsilon-isometries are close to isometries we obtain stability. An example is given showing that approximately orthogonality preserving mappings are in general far from scalar multiples of isometries, that is, stability does not hold.

• 出版日期2010-12-15