Translator Disclaimer
Autumn 2018 Compact and “compact” operators on standard Hilbert modules over $C^*$-algebras
Zlatko Lazović
Adv. Oper. Theory 3(4): 829-836 (Autumn 2018). DOI: 10.15352/aot.1806-1382

Abstract

We construct a topology on the standard Hilbert module $H_{\mathcal{A}}$ over a unital $C^*$-algebra and topology on $H_ \mathcal {A} ^{#}$ (the extension of the module $H_{\mathcal{A}}$ by the algebra $\mathcal{A}^{**}$) such that any “compact” operator (i.e. any operator in the norm closure of the linear span of the operators of the form $z\mapsto x \langle y,z \rangle$, $x,y\in H_{\mathcal{A}}$ (or $x,y \in H_ \mathcal {A} ^{#}$)) maps bounded sets into totally bounded sets.

Citation

Download Citation

Zlatko Lazović. "Compact and “compact” operators on standard Hilbert modules over $C^*$-algebras." Adv. Oper. Theory 3 (4) 829 - 836, Autumn 2018. https://doi.org/10.15352/aot.1806-1382

Information

Received: 12 June 2018; Accepted: 29 June 2018; Published: Autumn 2018
First available in Project Euclid: 7 July 2018

zbMATH: 06946381
MathSciNet: MR3856176
Digital Object Identifier: 10.15352/aot.1806-1382

Subjects:
Primary: 46L08
Secondary: 47B07

Rights: Copyright © 2018 Tusi Mathematical Research Group

JOURNAL ARTICLE
8 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.3 • No. 4 • Autumn 2018
Back to Top