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A non-unital $ ^\ast$-algebra has U$ C^{\ast}$NP if and only if its unitization has U$ C^{\ast}$NP


Authors: H. V. Dedania and H. J. Kanani
Journal: Proc. Amer. Math. Soc. 141 (2013), 3905-3909
MSC (2010): Primary 46K05; Secondary 46H05
DOI: https://doi.org/10.1090/S0002-9939-2013-11725-9
Published electronically: July 23, 2013
MathSciNet review: 3091779
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Abstract | References | Similar Articles | Additional Information

Abstract: The result stated in the title is proved, thereby disproving the result shown in a 1983 paper by B. A. Barnes (Theorem 4.1).


References [Enhancements On Off] (What's this?)

  • 1. J. Arhippainen and V. Müller, Norms on unitizations of Banach algebras revisited, Acta Math. Hungar., 114(3) (2007) 201-204. MR 2296542 (2007k:46081)
  • 2. B. A. Barnes, The properties of $ \ast $-regularity and uniqueness of $ C^{\ast }$-norm in a general $ \ast $-algebra, Trans. Amer. Math. Soc., 279(2) (1983) 841-859. MR 709587 (85f:46100)
  • 3. S. J. Bhatt and H. V. Dedania, Uniqueness of the uniform norm and adjoining identity in Banach algebras, Proc. Indian Acad. Sci. Math. Sci., 105(4)(1995) 405-409. MR 1409578 (97g:46062)
  • 4. P. A. Dabhi and H. V. Dedania, On the uniqueness of uniform norms and $ C^{\ast }$-norms, Studia Mathematica, 191(3)(2009) 263-270. MR 2481896 (2010c:46121)
  • 5. E. Kaniuth, A Course in Commutative Banach Algebras, Springer, New York, 2009. MR 2458901 (2010d:46064)
  • 6. T. W. Palmer, Banach Algebras and the General Theory of $ \ast $-algebras, Volumes I $ \&$ II, Cambridge University Press, 1994. MR 1270014 (95c:46002); MR 1819503 (2002e:46002)

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Additional Information

H. V. Dedania
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India
Email: hvdedania@yahoo.com

H. J. Kanani
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India
Email: hitenmaths69@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11725-9
Keywords: Non-commutative $\ast$-algebra, $C^{\ast}$-norm, spectral norm, $C^{\ast}$-algebra
Received by editor(s): August 8, 2011
Received by editor(s) in revised form: January 23, 2012
Published electronically: July 23, 2013
Additional Notes: This work has been supported by UGC-SAP-DRS-II Grant No. F.510/3/DRS/2009 provided to the Department of Mathematics, Sardar Patel University.
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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