Chapter

Functional Equations in Mathematical Analysis

Volume 52 of the series Springer Optimization and Its Applications pp 33-58

Date:

Orthogonality Preserving Property and its Ulam Stability

  • Jacek ChmielińskiAffiliated withInstytut Matematyki, Uniwersytet Pedagogiczny w Krakowie Email author 

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Abstract

We survey the results concerning the preservation (exact and approximate) of various types of orthogonality relations. We focus on the stability of the orthogonality preserving property. Our considerations are carried out in spaces with inner product structure as well as in normed spaces. Some related topics are also discussed.

Keywords

Orthogonality Birkhoff orthogonality Isosceles-orthogonality Approximate orthogonality Orthogonality preserving property Right-angle preserving property Linear preservers Stability Orthogonality equation Wigner equation Inner product spaces Hilbert modules Normed spaces Semi-innner product Norm derivatives Isometric mappings Approximate isometry