Talk:Banach algebra

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I cut "The algebra is unital if and only if the original space is compact. Also, since every continuous function on a compact space is automatically bounded, we do not need to assume the boundedness of the functions in this case." from the example "bounded continuous functions because the first sentance isn't true. The function identically 1 will be bounded and continuous on any space and act as a unit to this algebra (which is C(X) for X the stone-cech compactification of our original space). I think whoever added it was thinking of the continuous functions vanishing at infinity, for which the above would hold. A Geek Tragedy 16:50, 25 August 2006 (UTC)

What is a regular Banach algebra? A normal Banach algebra? Links to answers should possibly be added to the pages "normal" and "regular" too. --Tilin 11:59, 19 October 2006 (UTC)