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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
Published electronically: July 23, 2013
MathSciNet review: 3091779
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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).


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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.