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On Operator Sum and Product Adjoints and Closures

Published:2011-04-25
Printed: Sep 2011
• Karl Gustafson,
Department of Mathematics, University of Colorado at Boulder, Boulder, CO, U.S.A.
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Abstract

We comment on domain conditions that regulate when the adjoint of the sum or product of two unbounded operators is the sum or product of their adjoints, and related closure issues. The quantum mechanical problem PHP essentially selfadjoint for unbounded Hamiltonians is addressed, with new results.
 Keywords: unbounded operators, adjoints of sums and products, quantum mechanics
 MSC Classifications: 47A05 - General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

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