Character Density in Central Subalgebras of Compact Quantum Groups
2017 ◽
Vol 60
(3)
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pp. 449-461
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Keyword(s):
AbstractWe investigate quantum group generalizations of various density results from Fourier analysis on compact groups. In particular, we establish the density of characters in the space of fixed points of the conjugation action on L2(𝔾) and use this result to show the weak* density and normdensity of characters in ZL∞(G) and ZC(G), respectively. As a corollary, we partially answer an open question of Woronowicz. At the level of L1(G), we show that the center Z(L1(G)) is precisely the closed linear span of the quantum characters for a large class of compact quantum groups, including arbitrary compact Kac algebras. In the latter setting, we show, in addition, that Z(L1(G)) is a completely complemented Z(L1(G))-submodule of L1(G).
2016 ◽
Vol 2016
(711)
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1998 ◽
Vol 57
(1)
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pp. 73-91
2013 ◽
Vol 65
(5)
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pp. 1073-1094
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2014 ◽
Vol 57
(2)
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pp. 424-430
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2005 ◽
Vol 4
(1)
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pp. 135-173
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2016 ◽
Vol 68
(2)
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pp. 309-333
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2003 ◽
Vol 14
(08)
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pp. 865-884
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Vol 12
(03)
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pp. 289-338
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2014 ◽
Vol 57
(3)
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pp. 546-550
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