On the Adjoint and the Closure of the Sum of Two Unbounded Operators

Mortad, Mohammed Hichem

Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 498-505

Résumé

We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples “spice up” the paper.

Détail

DOI : 10.4153/CMB-2011-041-7

Mots-clés : 47A05, unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operators

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