Abstract
Indefinite inner product, which in the case of Kreĭn space is under control of a “symmetry” (=selfadjoint, unitary operator customarily denoted by J), can be treated in more relaxed way if the requirement of selfadjointness of J is dropped. Still in this case a Hilbert space is behind the scene and the role of J is to extend the range of methods which can be used for detecting diverse properties of the operators involved. A typical model on which many guesses can be done is an ℒ2(μ) space, where μ is a complex measure. In this paper I intend to build up a framework for the theory to be developed.
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Acknowledgement
The work is supported by the grant of NCN (National Science Center, Poland), decision No. DEC-2013/11/B/ST1/03613.
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Szafraniec, F.H. (2018). Dissymmetrising Inner Product Spaces. In: Alpay, D., Kirstein, B. (eds) Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations. Operator Theory: Advances and Applications(), vol 263. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68849-7_19
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DOI: https://doi.org/10.1007/978-3-319-68849-7_19
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