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

  Published:2011-03-11
 Printed: Sep 2011
  • Mohammed Hichem Mortad,
    Department of Mathematics, University of Oran Es-Senia, BP 1524 El Menouar, 31000 Oran, Algeria
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Abstract

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.
Keywords: unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operators unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operators
MSC Classifications: 47A05 show english descriptions General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A05 - General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
 

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