You need to clarify this problem a bit.

First, what is the domain space of the operator A? Is it C[–1,1] or is it C[0,1]? (It looks to me as though C[0,1] is a typo and that you meant to write C[–1,1] both times.)

Second, assuming that the domain space is C[–1,1], you have not specified the norm on that space. There are many different norms on the space C[–1,1], and the norm of the functional A will depend on the norm used in C[–1,1].