Napredna pretraga

## Approximately orthogonality preserving mappings on C*-modules

Ilišević, Dijana; Turnšek, Aleksej
Approximately orthogonality preserving mappings on C*-modules // Journal of Mathematical Analysis and Applications, 341 (2008), 1; 298-308 doi:10.1016/j.jmaa.2007.10.028 (međunarodna recenzija, članak, znanstveni)

Naslov
Approximately orthogonality preserving mappings on C*-modules

Autori
Ilišević, Dijana ; Turnšek, Aleksej

Izvornik
Journal of Mathematical Analysis and Applications (0022-247X) 341 (2008), 1; 298-308

Ključne riječi
Hilbert C*-module; approximate orthogonality; orthogonality preserving mapping; stability

Sažetak
We study orthogonality preserving and approximately orthogonality preserving mappings in the setting of inner product $C^*$-modules. In particular, if $V$ and $W$ are inner product $C^*$-modules over the $C^*$-algebra $\A,$ any $\A$-linear scalar multiple of an isometry is an $\A$-linear orthogonality preserving mapping. The converse does not hold in general, but it holds if $\A$ contains $\K(\H)$ (the $C^*$-algebra of all compact operators on a Hilbert space $\H$). Furthermore, we give the estimate of $\Vert \langle Tx, Ty \rangle - \Vert T \Vert^2 \langle x, y \rangle \Vert$ for an $\A$-linear approximately orthogonality preserving mapping $T : V \to W$ when $V$ and $W$ are inner product $C^*$-modules over a $C^*$-algebra containing $\K(\H)$. In the case $\A=\K(\H)$ and $V,$ $W$ are Hilbert, we also prove that an $\A$-linear approximately orthogonality preserving mapping can be approximated by an $\A$-linear orthogonality preserving mapping.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0372784-2757 - Preslikavanja na modulima nad prstenima, apstraktnim i operatorskim algebrama (Dijana Ilišević, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Dijana Ilišević, (228992)

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts