Naslov
Symmetrized Birkhoff–James orthogonality in arbitrary normed spaces

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

Izvornik
Journal of mathematical analysis and applications (0022-247X) 502 (2021), 1; 125203, 16

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Normed vector space ; Birkhoff–James orthogonality ; Graph diameter ; Clique number

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA