Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces [chapter]

Christian Mehl, André C.M. Ran, Leiba Rodman
Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems  
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
more » ... mal matrices to admit a polar decomposition or to admit a polar decomposition with commuting factors.
doi:10.1007/3-7643-7453-5_15 fatcat:jqvcxjiorvb6zkxcmegp6e6nkm