Talk:Dixmier trace
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Dixmier trace and Banach limit
[edit]It is not completely clear from the page why the indices have to be powers of 2, to obtain an example of a Dixmier trace from the Banach limit. Could someone comment? Katzmik (talk) 17:08, 7 January 2009 (UTC)
The scaling property as defined in the article, namely by doubling (i.e. writing it twice) each element in the sequence, guarantees that the Banach limit of the subsequence indexed by the powers of 2 will be the same (modulo a Markov shift), and therefore such a Banach limit will define a scale-invariant Dixmier trace. But why is scaling defined by doubling, rather than, say, tripling each term? What is the relevant property for applications? Katzmik (talk) 13:58, 8 January 2009 (UTC)