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On Square Roots and Logarithms of Self-Adjoint Operators
Published online by Cambridge University Press: 18 May 2009
Extract
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 if
A 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.
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- Copyright © Glasgow Mathematical Journal Trust 1958
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