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It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness… Click to show full abstract
It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness condition in one of J. Chmieliński’s results. Further characterizations of inner product spaces are obtained by studying properties of linear operators related to Birkhoff orthogonality and isosceles orthogonality.
Keywords:
product spaces;
product;
inner product;
orthogonalities linear;
linear operators;
operators characterization
Journal Title: Aequationes mathematicae
Year Published: 2017
Link to full text (if available)
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Journal Title: Aequationes mathematicae
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!