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Adjoints and formal adjoints of matrices of unbounded operators

Authors: Manfred Möller and Franciszek Hugon Szafraniec
Journal: Proc. Amer. Math. Soc. 136 (2008), 2165-2176
MSC (2000): Primary 47A05; Secondary 47D06
Published electronically: February 14, 2008
MathSciNet review: 2383522
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Abstract: In this paper we discuss diverse aspects of the mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter as it is the troublemaker.

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Manfred Möller
Affiliation: The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, WITS, 2050, South Africa

Franciszek Hugon Szafraniec
Affiliation: Instytut Mathematyki, Uniwersytet Jagielloński, ul. Reymonta 4, Pl-30059 Kraków, Poland

Keywords: Operator matrix, row operator, column operator, adjoint and formal adjoint
Received by editor(s): December 11, 2006
Received by editor(s) in revised form: April 27, 2007
Published electronically: February 14, 2008
Additional Notes: This work was supported by a grant of the NRF of South Africa, GUN 2053746, and by the grant KBN 2 P 03A 637 024 (Poland).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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