On Square Roots and Logarithms of Self-Adjoint Operators

Abstract

All operators considered in this paper are bounded and linear (everywhere defined) on a Hilbert space. An operator A will be called a square root of an operator B ifA simple sufficient condition guaranteeing that any solution A of (1) be normal whenever B is normal was obtained in [1], namely: If B is normal and if there exists some real angle θ for which Re(Aeιθ)≥0, then (1) implies that A is normal. Here, Re (C) denotes the real part ½(C + C*) of an operator C.