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  • Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces
    Arambašić, Ljiljana ...
    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.
    Source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 502, iss. 1, Oct. 2021, art. 125203 (16 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2021
    Language - english
    COBISS.SI-ID - 105771267

    Link(s):

    https://www.sciencedirect.com/science/article/abs/pii/S0022247X21002821
    DOI

source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 502, iss. 1, Oct. 2021, art. 125203 (16 str.))

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