Abstract
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
Mathematics Subject Classification (2010). Primary 47A10, 47B44; Secondary 46E20, 46F05.
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Arlinskiĭ, Y., Belyi, S. (2014). Non-negative Self-adjoint Extensions in Rigged Hilbert Space. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_2
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