What does Birkhoff-James orthogonality know about the norm?
Ljiljana Aramba\v{s}i\'c, Alexander Guterman, Bojan Kuzma, Rajna, Raji\'c, and Svetlana Zhilina
TL;DR
This paper demonstrates that Birkhoff-James orthogonality fully characterizes smooth norms in reflexive Banach spaces and can determine the dimensions of these spaces.
Contribution
It reveals that Birkhoff-James orthogonality encodes complete information about smooth norms and the dimensions of reflexive Banach spaces, providing new insights into their structure.
Findings
Birkhoff-James orthogonality characterizes smooth norms in reflexive Banach spaces.
It can be used to compute the dimensions of the underlying normed spaces.
The results deepen understanding of the relationship between orthogonality and space geometry.
Abstract
It is shown that Birkhoff-James orthogonality knows everything about the smooth norms in reflexive Banach spaces and can also compute the dimensions of the underlying normed spaces.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Constraint Satisfaction and Optimization