Fractional powers of the algebraic sum of normal operators

Diagana, Toka

doi:10.1090/S0002-9939-05-08183-9

Fractional powers of the algebraic sum of normal operators
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by Toka Diagana

Proc. Amer. Math. Soc. 134 (2006), 1777-1782

DOI: https://doi.org/10.1090/S0002-9939-05-08183-9

Published electronically: December 15, 2005

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Abstract:

The main concern in this paper is to give sufficient conditions such that if $A, B$ are unbounded normal operators on a (complex) Hilbert space $\mathbb H$, then for each $\alpha \in (0 , 1)$, the domain $D((\overline {A+B})^{\alpha })$ equals $D(A^{\alpha }) \cap D(B^{\alpha })$. It is then verified that such a result can be applied to characterize the domains of fractional powers of a large class of the Hamiltonians with singular potentials arising in quantum mechanics through the study of the Schrödinger equation.

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