Matrix symbol of order two for some Banach algebras

Two classes of Banach algebras which admit a matrix symbol of order 2 are d escribed, and an explicit form of the symbol is obtained. Also we describe all polynomials F(X, Y) and F(X, Y, Z) such that the norms of polynomials F (B, B*) ( when B-2 = 0) and F(S, W, W*) (when S-2 = I, W-2 = 0, S* = S) dep end only on the polynomial F and on the norms parallel toB parallel to, par allel toW parallel to. Applications to Banach algebras generated by singula r integral operators and some their perturbations are considered.