Talk:Composition operator

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 Field:  Analysis

confusion[edit]

I'm not sure if it is justified to call "composition operator" the operator C_g rather than the operator "o" itself. To be not too invasive, I just added a kind of "otheruse" preamble, but maybe one should go a bit further (I think more people would think of "o" rather than of Cg when they hear "composition operator" in a general context.) — MFH:Talk 18:31, 16 October 2006 (UTC)

yes, this confused me. If I have a function g o f then I guess g and f are operands of the operator "o". I guess just f is an operand of the operation C_g(f)? If so (and this is what I really want to know) what do we call g? Perhaps a parameterized operand of the operator C?220.253.85.77 03:56, 26 April 2007 (UTC)
Uh, no. C_g is a linear operator, it is the thing that is studied. The fact that is linear is what allows it to be studied as such, in operator theory. By contrast, composition 'o' is not linear, and is thus strictly speaking not an "operator", at least, not the kind studied in operator theory. Err. well, I guess you could call 'o' 'nonlinear' or something like that, but that misses the point. linas (talk) 04:22, 14 November 2010 (UTC)