Communications of the
Korean Mathematical Society CKMS

In this article, we show that if $T\in \mathcal{B}(H)$ is an antinormal operator, $M$ is a reducing subspace for $T$ and $i(T|_M)$ and $i(T)$ are of the same sign, then $T|_M$ is also antinormal. We also characterize the antinormality of composition operators on $L^2(X)$ for a $\sigma$-finite measure space $X$.

Keywords: Composition operator, antinormal operator, index of an operator, Fredholm operator

MSC numbers: 47A05, 47A53, 47B37