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Proceedings of the American Mathematical Society

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Norms on unitizations of Banach algebras


Authors: A. K. Gaur and Z. V. Kovářík
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
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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.


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  • [1] 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
  • [2] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
  • [3] 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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1104395-1
Keywords: Banach algebra, unitization, equivalent norms, Hermitian element
Article copyright: © Copyright 1993 American Mathematical Society