$C^*$ -algebra structure on certain Banach algebra products. Issue 3 (7th September 2020)
- Record Type:
- Journal Article
- Title:
- $C^*$ -algebra structure on certain Banach algebra products. Issue 3 (7th September 2020)
- Main Title:
- $C^*$ -algebra structure on certain Banach algebra products
- Authors:
- Abtahi, Fatemeh
- Abstract:
- Abstract: Let $\mathcal A$ and $\mathcal B$ be commutative and semisimple Banach algebras and let $\theta \in \Delta (\mathcal B)$ . In this paper, we prove that $\mathcal A\times _{\theta }\mathcal B$ is a type I-BSE algebra if and only if ${\mathcal A}_e$ and $\mathcal B$ are so. As a main application of this result, we prove that $\mathcal A\times _{\theta }\mathcal B$ is isomorphic with a $C^*$ -algebra if and only if ${\mathcal A}_e$ and $\mathcal B$ are isomorphic with $C^* $ -algebras. Moreover, we derive related results for the case where $\mathcal A$ is unital.
- Is Part Of:
- Canadian mathematical bulletin =. Volume 64:Issue 3(2021)
- Journal:
- Canadian mathematical bulletin =
- Issue:
- Volume 64:Issue 3(2021)
- Issue Display:
- Volume 64, Issue 3 (2021)
- Year:
- 2021
- Volume:
- 64
- Issue:
- 3
- Issue Sort Value:
- 2021-0064-0003-0000
- Page Start:
- 678
- Page End:
- 686
- Publication Date:
- 2020-09-07
- Subjects:
- 46J05 -- 46J25
BSE-algebra -- BSE-function -- C*-algebra -- commutative Banach algebra -- multiplier algebra -- θ-product
Mathematics -- Periodicals
Mathematics
Periodicals
510.5 - Journal URLs:
- http://www.cms.math.ca/cmb/ ↗
https://www.cambridge.org/core/journals/canadian-mathematical-bulletin ↗ - DOI:
- 10.4153/S0008439520000740 ↗
- Languages:
- English
- ISSNs:
- 0008-4395
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 19079.xml