On left and right decomposably regular operators

Abstract

Let $B(X, Y)$ denote the set of all bounded linear operators from Banach space $X$ to Banach space $Y$. In this paper, we introduce the concepts of left and right decomposably regular operators, left and right decomposably Fredholm operators in the setting of $B(X, Y)$, and the corresponding holomorphic versions in the setting of $B(X)$. By using Harte's techniques, we obtain various characterizations of these classes of operators. As the applications of these characterizations, we can compute the topological interiors and closures of them.