A noncommutative Brooks-Jewett Theorem |
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Authors: | E Chetcuti J Hamhalter |
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Institution: | a Department of Mathematics, Faculty of Science, University of Malta, Msida MSD 06, Malta b Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Prague 6, Czech Republic |
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Abstract: | In classical measure theory the Brooks-Jewett Theorem provides a finitely-additive-analogue to the Vitali-Hahn-Saks Theorem. In this paper, it is studied whether the Brooks-Jewett Theorem allows for a noncommutative extension. It will be seen that, in general, a bona-fide extension is not valid. Indeed, it will be shown that a C*-algebra A satisfies the Brooks-Jewett property if, and only if, it is Grothendieck, and every irreducible representation of A is finite-dimensional; and a von Neumann algebra satisfies the Brooks-Jewett property if, and only if, it is topologically equivalent to an abelian algebra. |
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Keywords: | _method=retrieve& _eid=1-s2 0-S0022247X0900153X& _mathId=si2 gif& _pii=S0022247X0900153X& _issn=0022247X& _acct=C000053510& _version=1& _userid=1524097& md5=fb063f463ddf11ef79cb14c2459a5fd4')" style="cursor:pointer C*-algebra" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">C*-algebra von Neumann algebra Brooks-Jewett property Vitali-Hahn-Saks property |
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