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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fractional powers of the algebraic sum of normal operators


Author: Toka Diagana
Journal: Proc. Amer. Math. Soc. 134 (2006), 1777-1782
MSC (2000): Primary 47B44, 47B25, 47B15
Published electronically: December 15, 2005
MathSciNet review: 2207493
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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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Additional Information

Toka Diagana
Affiliation: Department of Mathematics, Howard University, 2441 6th Street N.W., Washington D.C. 20059
Email: tdiagana@howard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08183-9
PII: S 0002-9939(05)08183-9
Keywords: Normal operator, self-adjoint operator, nonnegative operator, fractional powers of operators, algebraic sum, form sum, Hamiltonian, singular potentials
Received by editor(s): July 12, 2004
Received by editor(s) in revised form: January 31, 2005
Published electronically: December 15, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society