Abstract
Let A be an algebra without unit. If ∥ ∥ is a complete regular norm on A it is known that among the regular extensions of ∥ ∥ to the unitization of A there exists a minimal (operator extension) and maximal (ℓ1-extension) which are known to be equivalent. We shall show that the best upper bound for the ratio of these two extensions is exactly 3. This improves the results represented by A. K. Gaur and Z. V. Kovářík and later by T. W. Palmer.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. K. Gaur and Z. V. Kovářík, Norms, states and numerical ranges on direct sums, Analysis, 11 (1991), 155–164.
A. K. Gaur and Z. V. Kovářík, Norms on unitizations of Banach algebras, Proc. Amer. Math. Soc., 117 (1993), 111–113.
T. W. Palmer, review MR1104395, Mathematical Reviews 93c:46082.
T. W. Palmer, Banach Algebras and The General Theory of *-Algebras, Vol 1, Cambridge University Press (NY, 1994).
Author information
Authors and Affiliations
Additional information
The second author was partially supported by the grant No. 201/03/0041 of GAČR.
Rights and permissions
About this article
Cite this article
Arhippainen, J., Müller, V. Norms on unitizations of banach algebras revisited. Acta Math Hung 114, 201–204 (2007). https://doi.org/10.1007/s10474-006-0524-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-006-0524-8