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Banach algebras with unique uniform norm


Authors: S. J. Bhatt and H. V. Dedania
Journal: Proc. Amer. Math. Soc. 124 (1996), 579-584
MSC (1991): Primary 46J05
DOI: https://doi.org/10.1090/S0002-9939-96-03063-8
MathSciNet review: 1301488
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Abstract: Commutative semisimple Banach algebras that admit exactly one uniform norm (not necessarily complete) are investigated. This unique uniform norm property is completely characterized in terms of each of spectral radius, Silov boundary, set of uniqueness, semisimple norms; and its connection with recently investigated concepts like spectral extension property, multiplicative Hahn Banach extension property and permanent radius are revealed. Several classes of Banach algebras having this property as well as those not having this property are discussed.


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Additional Information

S. J. Bhatt
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India

H. V. Dedania
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India
Address at time of publication: Department of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

DOI: https://doi.org/10.1090/S0002-9939-96-03063-8
Keywords: Unique uniform norm property, semisimple norm, spectral extension property, spectral norm, extension of Banach algebra, unique semisimple norm property
Received by editor(s): May 16, 1994
Received by editor(s) in revised form: September 12, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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