Niigata Prefectural Nagaoka High School

We study unital homomorphisms between Banach algebras of vector-valued maps including Banach algebras of Lipschitz maps with values in unital commutative Banach algebras. We provide sufficient conditions under which every unital homomorphism or isomorphis

S7%: xk = cosOk, Ok = ( 2 k 1)r/(2n), k = 1 , 2 , . . . , n . Let f E C[-1,1] , and let L?%[f; x] be the Lagrange interpolatory polynomial corresponding to the abscissas S7%. If f (x ) has the modulus of continuity w(e) = o(I l o g ( e ) l 1 ) , then L?%[f;x] ~ f ( x ) , 1 < x < 1 (see [5, p. 3371). On the other hand, if we consider the Hermite-Fej~r interpolatory polynomial H2n-l[f; x,] of degree 2 n 1 such that