Abstract
ABSTRACT We study a new class of Hilbert space operators, named C-normal operators for C a conjugation on a complex Hilbert space , which were introduced by M. Ptak, K. Simik and A. Wicher. We provide a refined polar decomposition of C-normal operators. It is proved that those invertible ones are norm dense in and each contraction in is a mean of two unitary ones. For a dense class of operators, we prove that their C-normality coincides with C-symmetry. Also some illustrating examples are provided to show that is not closed under several natural operations.
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