Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces
Christian Mehl, André C. M. Ran, Leiba Rodman · Birkhäuser-Verlag eBooks · 2006
Polar decompositions of normal matrices in indefinite inner product spaces are studied. The main result of this paper provides sufficient conditions for a normal operator in a Krein space to admit a polar decomposition. As an application of this result, we show that any normal matrix in a finite-dimensional indefinite inner product space admits a polar decomposition which answers affirmatively an open question formulated in [2]. Furthermore, necessary and sufficient conditions are given for a matrix to admit a polar decomposition and for a normal matrix to admit a polar decomposition with commuting factors.