NDLI: Mappings approximately preserving orthogonality in normed spaces

Content Provider	Semantic Scholar
Author	Mojskerc, Blaz Turnsek, A. J. Branko
Copyright Year	2010
Abstract	Abstract 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 e -isometry. Thus, whenever e -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.
Starting Page	3821
Ending Page	3831
Page Count	11
File Format	PDF HTM / HTML
DOI	10.1016/j.na.2010.08.007
Alternate Webpage(s)	https://web.math.pmf.unizg.hr/OSAM/abstracts/Turnsek.pdf
Alternate Webpage(s)	https://doi.org/10.1016/j.na.2010.08.007
Volume Number	73
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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