Symmetrized Birkhoff–James orthogonality in arbitrary normed spaces

Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma, Rajna Rajić, Svetlana Zhilina

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Graph defined by Birkhoff–James orthogonality relation in normed spaces is studied. It is shown that (i) in a normed space of sufficiently large dimension there always exists a nonzero vector which is mutually Birkhoff–James orthogonal to each among a fixed number of given vectors, and (ii) in nonsmooth norms the cardinality of the set of pairwise Birkhoff–James orthogonal vectors may exceed the dimension of the vector space, but this cardinality is always bounded above by a function of the dimension. It is further shown that any given pair of elements in a normed space can be extended to a finite tuple such that each consecutive elements are mutually Birkhoff–James orthogonal; the exact minimal length of the tuple is also determined.

Original languageEnglish
Article number125203
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Oct 2021
Externally publishedYes

Bibliographical note

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© 2021 Elsevier Inc.


  • Birkhoff–James orthogonality
  • Clique number
  • Graph diameter
  • Normed vector space


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