Polar decompositions and related classes of operators in spaces ∏ κ
Tóm tắt
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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