Norms on unitizations of Banach algebras
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- by A. K. Gaur and Z. V. Kovářík PDF
- Proc. Amer. Math. Soc. 117 (1993), 111-113 Request permission
Abstract:
Equivalence of various norms on the unitization of a nonunital Banach algebra is established, with bounds ($1$ and $6\exp (1)$) uniform over the class of such algebras. A tighter bound, $3$, is obtained in ${C^{\ast }}$-algebras for elements with Hermitian nonunital parts.References
- F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, vol. 2, Cambridge University Press, London-New York, 1971. MR 0288583 N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
- Abhay K. Gaur and Zdislav V. Kovářík, Norms, states and numerical ranges on direct sums, Analysis 11 (1991), no. 2-3, 155–164. MR 1143631, DOI 10.1524/anly.1991.11.23.155
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 111-113
- MSC: Primary 46H05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1104395-1
- MathSciNet review: 1104395