Normal Singular Integral Operators with Cauchy Kernel on L.

Let α and β be functions in $${L^\infty(\mathbb{T})}$$ , where $${\mathbb{T}}$$ is the unit circle. Let P denote the orthogonal projection from $${L^2(\mathbb{T})}$$ onto the Hardy space $${H^2(\mathbb{T})}$$ , and Q = I − P, where I is the identity operator on $${L^2(\mathbb{T})}$$ . This paper is concerned with the singular integral operators S on $${L^2(\mathbb{T})}$$ of the form S f = αPf + βQf, for $${f \in L^2(\mathbb{T})}$$ . In this paper, we study the normality of S which is related to the Brown-Halmos theorem for the normal Toeplitz operator on $${H^2(\mathbb{T})}$$ . [ABSTRACT FROM AUTHOR]