Linear mappings approximately preserving orthogonality
By J. Chmieliński. 2005
78 citations recorded by the source corpus.
Abstract We consider the class of linear mappings, between real or complex inner product spaces, such that for each two orthogonal vectors in the domain their values are ɛ-orthogonal in the target space. By ɛ-orthogonality ( 0 ⩽ ɛ 1 ) we mean the relation u ⊥ ɛ v ⇔ | 〈 u | v 〉 | ⩽ ɛ ‖ u ‖ ‖ v ‖ .
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/adf96eadd3e8b0666f4ba44692cc277b1cc39498
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In Applied Mathematics
Citations in the corpus
- On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces (2012, background): “[33]) that an orthogonality preserving linear map between two inner product spaces is necessarily a scalar multiple of a linear isometry.”