Journal of Operator Theory

Volume 44, Issue 2, Fall 2000 pp. 243-254.

Adjoints, absolute values and polar decompositions

Authors: Douglas Bridges (1), Fred Richman (2), and Peter Schuster (3)
Author institution: (1) Department of Mathematics & Statistics, University of Canterbury, Christchurch, New Zealand
(2) Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA
(3) Mathematisches Institut der Universitaet, Theresienstrasse 39, 80333 Munchen, Germany

Summary: Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the existence of an adjoint, and a general notion of a polar decomposition is developed. The Riesz representation theorem is proved without countable choice.

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