Abstract
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.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Mehl, C., Ran, A.C., Rodman, L. (2005). Polar Decompositions of Normal Operators in Indefinite Inner Product Spaces. In: Förster, KH., Jonas, P., Langer, H. (eds) Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory: Advances and Applications, vol 162. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7453-5_15
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DOI: https://doi.org/10.1007/3-7643-7453-5_15
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7452-5
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