Positive Operators and Plus-operators in Krein Spaces
Positive operators in a Krein space (Sections 1 and 3) have turned out (see Chapter VIII, especially Section 6 and the Notes) to be the most fruitful generalizations of positive operators in Hilbert space. In Section 2 an alternative extension of the latter concept is considered. Sections 4–6 resume the study of plus-operators begun in Section II.8. A unifying feature of the chapter is the repeated application of the Schwarz inequality. Theorems 1.3, 3.1, 5.2, 5.4, 5.5 and 6.1 deserve particular attention.
KeywordsPositive Operator Selfadjoint Operator Krein Space Fundamental Symmetry Alternative Extension
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