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Published in:
2014 | OriginalPaper | Chapter
Non-negative Self-adjoint Extensions in Rigged Hilbert Space
Authors : Yury Arlinskiĭ, Sergey Belyi
Published in: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation
Publisher: Springer Basel
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We study non-negative self-adjoint extensions of a non densely defined non-negative symmetric operator Å with the exit in the rigged Hilbert space constructed by means of the adjoint operator Å
*
(bi-extensions). Criteria of existence and descriptions of such extensions and associated closed forms are obtained. Moreover, we introduce the concept of an extremal nonnegative bi-extension and provide its complete description. After that we state and prove the existence and uniqueness results for extremal non-negative biextensions in terms of the Kreĭn–von Neumann and Friedrichs extensions of a given non-negative symmetric operator. Further, the connections between positive boundary triplets and non-negative self-adjoint bi-extensions are presented