Symmetrized Birkhoff–James orthogonality in arbitrary normed spaces (CROSBI ID 295561)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Arambašić, Ljiljana ; Guterman, Alexander ; Kuzma, Bojan ; Rajić, Rajna ; Zhilina, Svetlana
engleski
Symmetrized Birkhoff–James orthogonality in arbitrary normed spaces
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.
Normed vector space ; Birkhoff–James orthogonality ; Graph diameter ; Clique number
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Podaci o izdanju
502 (1)
2021.
125203
16
objavljeno
0022-247X
1096-0813
10.1016/j.jmaa.2021.125203