Quark–lepton complementarity: Difference between revisions

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A '''Banach *-algebra''' ''A'' is a [[Banach algebra]] over the field of [[complex number]]s, together with a map * : ''A'' → ''A'' called ''[[Involution (mathematics)|involution]]'' which has the following properties:
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# (''x'' + ''y'')* = ''x''* + ''y''* for all ''x'', ''y'' in ''A''.
# <math>(\lambda x)^* = \bar{\lambda}x^*</math> for every λ in '''C''' and every ''x'' in ''A''; here, <math>\bar{\lambda}</math> denotes the complex conjugate of λ.
# (''xy'')* = ''y''* ''x''* for all ''x'', ''y'' in ''A''.
# (''x''*)* = ''x'' for all ''x'' in ''A''.
 
In most natural examples, one also has that the involution is [[isometry|isometric]], i.e.
* ||''x''*|| = ||''x''||,
 
==See also==
*[[Algebra over a field]]
*[[Associative algebra]]
*[[*-algebra]]
*[[C*-algebra]].
 
[[Category:Banach algebras]]

Latest revision as of 15:39, 14 February 2014

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