Population model - Revision history

en>AussieLegend: added navbox

2014-06-25T03:56:00Z

added navbox

← Older revision		Revision as of 05:56, 25 June 2014
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	~~A [[Banach algebra]],~~ ''A'', is '''amenable''' if all [[bounded linear map\|bounded]] [[Differential algebra\|derivation]]s from ''A'' into [[dual module\|dual]] [[Banach module\|Banach ''A''-bimodules]] are [[inner derivation\|inner]] (that is of the form <math>a\mapsto a.x-x.a</math> for some <math>x</math> in ~~the dual module)~~.		Friends call him Royal Cummins. I've usually cherished living in Idaho. What she loves doing is to play croquet but she hasn't produced a dime with it. Managing individuals is what I do in my working day job.<br><br>Feel free to visit my site - extended car warranty ([http://Roki-Gaming.de/index.php?mod=users&action=view&id=371 visit the up coming website])

	~~An equivalent characterization~~ is ~~that~~ '~~'A'' is amenable if and only if~~ it ~~has a [[virtual diagonal]]~~.

	~~==Examples==~~
	* If ''A'' is ~~a [[group algebra]]~~ <~~math~~>~~L^1(G)~~<~~/math~~> ~~for some [[locally compact group]] ''G'' then ''A'' is amenable if and only if ''G'' is [[amenable group\|amenable]].~~
	~~* If ''A'' is a [[C~~-~~algebra]] then ''A'' is amenable if and only if it is~~ [[nuclear C-~~algebra\|nuclear]].~~
	* If ''A'' is a [[uniform algebra]] on a [[compact space\|compact]] [[Hausdorff space]] then ''A'' is amenable if and only if it is trivial (i.e. the algebra ''C(X)'' of all [[continuous function\|continuous]] [[complex number\|complex]] [[function (mathematics)\|functions]] on ''X'').
	* If ''A'' is amenable and there is a continuous algebra homomorphism <math>\theta</~~math> from ''A'' to another Banach algebra, then the closure of <math>\theta(A)</math> is amenable~~.

	==~~References~~==
	* F.F. Bonsall, J. Duncan, "Complete normed algebras", Springer-Verlag (1973).
	* H.G. Dales, "Banach algebras and automatic continuity", Oxford University Press (2001).
	* B.E. Johnson, "Cohomology in Banach algebras", Memoirs of the ~~AMS '''127''' (1972).~~
	* J.-P. Pier, "Amenable Banach algebras", Longman Scientific and Technical (1988).

	~~{{Mathanalysis-stub}}~~

	~~[[Category:Banach algebras]]~~

en>Kku: lx

2014-01-21T15:43:30Z

← Older revision		Revision as of 17:43, 21 January 2014
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	~~The author~~ is ~~called Araceli Gulledge~~. ~~Kansas is our beginning location and my mothers and fathers live close by~~. ~~Interviewing is what I do~~ in ~~my day job~~. ~~What she loves doing~~ is ~~bottle tops collecting~~ and ~~she is trying to make~~ it a ~~occupation~~.<br><br>~~My blog post:~~ [~~http://Www~~.~~Neonex~~.cl/~~Default~~.~~aspx?tabid~~=~~61&userId~~=~~4739 Www~~.~~Neonex~~.cl]		A [[Banach algebra]], ''A'', is '''amenable''' if all [[bounded linear map\|bounded]] [[Differential algebra\|derivation]]s from ''A'' into [[dual module\|dual]] [[Banach module\|Banach ''A''-bimodules]] are [[inner derivation\|inner]] (that is of the form <math>a\mapsto a.x-x.a</math> for some <math>x</math> in the dual module).

			An equivalent characterization is that ''A'' is amenable if and only if it has a [[virtual diagonal]].

			==Examples==
			* If ''A'' is a [[group algebra]] <math>L^1(G)</math> for some [[locally compact group]] ''G'' then ''A'' is amenable if and only if ''G'' is [[amenable group\|amenable]].
			* If ''A'' is a [[C-algebra]] then ''A'' is amenable if and only if it is [[nuclear C-algebra\|nuclear]].
			* If ''A'' is a [[uniform algebra]] on a [[compact space\|compact]] [[Hausdorff space]] then ''A'' is amenable if and only if it is trivial (i.e. the algebra ''C(X)'' of all [[continuous function\|continuous]] [[complex number\|complex]] [[function (mathematics)\|functions]] on ''X'').
			* If ''A'' is amenable and there is a continuous algebra homomorphism <math>\theta</math> from ''A'' to another Banach algebra, then the closure of <math>\theta(A)</math> is amenable.

			==References==
			* F.F. Bonsall, J. Duncan, "Complete normed algebras", Springer-Verlag (1973).
			* H.G. Dales, "Banach algebras and automatic continuity", Oxford University Press (2001).
			* B.E. Johnson, "Cohomology in Banach algebras", Memoirs of the AMS '''127''' (1972).
			* J.-P. Pier, "Amenable Banach algebras", Longman Scientific and Technical (1988).

			{{Mathanalysis-stub}}

			[[Category:Banach algebras]]

en>Melcombe: /* History */ add wikilinks, remove unnecessary capitals

2012-04-13T15:33:03Z

History: add wikilinks, remove unnecessary capitals

New page

The author is called Araceli Gulledge. Kansas is our beginning location and my mothers and fathers live close by. Interviewing is what I do in my day job. What she loves doing is bottle tops collecting and she is trying to make it a occupation.<br><br>My blog post: [http://Www.Neonex.cl/Default.aspx?tabid=61&userId=4739 Www.Neonex.cl]