Naslov
Strong Birkhoff-James orthogonality in Hilbert C*- modules

Autori
Arambašić, Ljiljana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
Hilbert C*-Modules Online Weekend

Mjesto i datum
Njemačka; Ruska Federacija, 05.12.2020. - 06.12.2020

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
strong Birkhoff-James orthogonality, C*-algebra

Sažetak
We say that two elements of a Hilbert C*-module are orthogonal if their C*-valued inner product is 0. In a Hilbert C*-module, besides this type of orthogonality, we can study all other orthogonalities defined in a general normed space. One which is most frequently used is Birkhoff–James orthogonality - if x, y are elements of a normed linear space X, then x is orthogonal to y in the BJ sense if ∥x + λy∥ ≥ ∥x∥ for all scalars λ. As we usually do in Hilbert C*-modules, we study analogous relations obtained by replacing scalars with elements of the underlying C*- algebra, or the norm with the C*- valued ”norm”. It often happens that these relations are very strong and coincide with (the first mentioned) orthogonality in a Hilbert C*- module, but not always. This leads to the notion of the strong (also called modular) BJ orthogonality which is the main topic of this talk. This is a joint work with A. Guterman, B. Kuzma, R. Rajić and S. Zhilina.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA