Abstract
Let φ be ab ounded linear functional on A ,w hereA is a commutative Banach algebra, then the bilinear functional ˇ φ is defined as ˇ φ(a, b )= φ(ab) − φ(a)φ(b )f or eacha and b in A .I f thenorm of ˇ φ is small then φ is approximately multiplicative, and it is of interest whether or not � ˇ φ� being small implies that φ is near to a multiplicative functional. If this property holds for a commutative Banach algebra then A is an AMNM algebra (approximately multiplicative functionals are near multiplicative functionals). The main result of the paper shows that C N [0, 1] M (the complex valued functions defined on [0, 1] M with all Nth order partial derivatives continuous) is AMNM. It is also shown that a similar proof can be applied to certain Lipschitz algebras.
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