Positive Operators and Plus-operators in Krein Spaces

  • János Bognár
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 78)


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.


Positive Operator Selfadjoint Operator Krein Space Fundamental Symmetry Alternative Extension 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • János Bognár
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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