Izvorni znanstveni članak

https://doi.org/10.3336/gm.57.1.05

Approximately orthogonality preserving mappings on Hilbert C_{0}(Z)-modules

Mohammad B Asadi ; School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Zahra Hassanpour Yakhdani ; School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
Fatemeh Olyaninezhad ; Department of Mathematics, University of Guilan, Rasht, Guilan, Iran
Abbas Sahleh ; Department of Mathematics, University of Guilan, Rasht, Guilan, Iran

Preuzmi JATS datoteku

Sažetak

In this paper, we will use the categorical approach to
Hilbert \(C^{\ast}\)-modules over a commutative \(C^{\ast}\)-algebra
to investigate the approximately orthogonality preserving mappings
on Hilbert \(C^{\ast}\)-modules over a commutative
\(C^{\ast}\)-algebra.

Indeed, we show that if \(\Psi:\Gamma \rightarrow \Gamma^{\prime}
\) is a nonzero \( C_{0}(Z) \)-linear
\(( \delta , \varepsilon)\)-orthogonality preserving mapping
between the continuous fields of Hilbert spaces on a locally
compact Hausdorff space \(Z\), then \(\Psi\) is injective, continuous
and also for every \( x, y \in \Gamma \) and \(z \in Z\),
\[



\vert
\langle \Psi(x),\Psi(y) \rangle(z) - \varphi^2(z) \langle x,y
\rangle(z) \vert \leq \frac{4(\varepsilon -
\delta)}{(1-\delta)(1+\varepsilon)} \Vert \Psi(x) \Vert \Vert
\Psi(y) \Vert,


\]
where \(\varphi(z) = \sup \{ \Vert \Psi(u)(z)
\Vert : u ~ \text{is a unit vector in} ~ \Gamma \}\).

Ključne riječi

Approximately orthogonality preserving, Hilbert\(C^*\)-module, Continuous field of Hilbert spaces

Hrčak ID:

279800

URI

https://hrcak.srce.hr/279800

Datum izdavanja:

28.6.2022.

Posjeta: 772 *