Orthogonality preserving property and its Ulam stability. (English) Zbl 1248.39023
Rassias, Themistocles M. (ed.) et al., Functional equations in mathematical analysis. Dedicated to the memory of Stanisław Marcin Ulam on the occasion of the 100th anniversary of his birth. Berlin: Springer (ISBN 978-1-4614-0054-7/hbk; 978-1-4614-0055-4/ebook). Springer Optimization and Its Applications 52, 33-58 (2011).
Summary: 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.
For the entire collection see [Zbl 1225.39001].
For the entire collection see [Zbl 1225.39001].
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 39B55 | Orthogonal additivity and other conditional functional equations |
| 47B49 | Transformers, preservers (linear operators on spaces of linear operators) |
