Abstract
Polar decompositions with respect to an indefinite inner product are studied for bounded linear operators acting on a ∏ κ space. Criteria are given for existence of various forms of the polar decompositions, under the conditions that the range of a given operatorX is closed and that zero is not an irregular critical point of the selfadjoint operatorX [*]X. Both real and complex spaces ∏ κ are considered. Relevant classes of operators having a selfadjoint (in the sense of the indefinite inner product) square root, or a selfadjoint logarithm, are characterized.
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The work of this author was partially supported by INdAM-GNCS and MURST
The work of this author was partially supported by NSF grant DMS-9988579.