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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 Math. Soc. Lecture Notes Ser., vol. 2, Cambridge Univ. Press, Cambridge and New York, 1971. MR 0288583 (44:5779)
  • [2] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
  • [3] A. K. Gaur and Z. V. Kovářík, Norms, states and numerical ranges on direct sums, Analysis, Internat. Math. J. Anal. Appl. 11 (1991), 155-164. MR 1143631 (92k:46078)

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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

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