Introduction. The purpose of this paper is to study noncommutative C*algebras as Banach spaces. The Gelfand representation of an abelian C*-algebra as the algebra of all continuous complex-valued functions on its spectrum has made it possible to apply the techniques of measure theory and the topological properties of compact Hausdorff spaces to the study of such algebras. No such structure theo...

We combine the Riemann-Hilbert approach with the techniques of Banach algebras to obtain an extension of Baxter’s Theorem for polynomials orthogonal on the unit circle. This is accomplished by using the link between the negative Fourier coefficients of the scattering function and the coefficients in the recurrence formula satisfied by these polynomials.

In [6], Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras.

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

we investigate the stability of generalizedderivations on banach algebras with a bounded central approximateidentity. we show that every approximate generalized derivation inthe sense of rassias, is an exact generalized derivation. also thestability problem of generalized derivations on the faithful banachalgebras is investigated.

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...