Weak-operator Continuity and the Existence of Adjoints

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Mathematical Logic Quarterly 45 (2):203-206 (1999)
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Abstract

It is shown, within constructive mathematics, that the unit ball B1 of the set of bounded operators on a Hilbert space H is weak-operator totally bounded. This result is then used to prove that the weak-operator continuity of the mapping T → AT on B1 is equivalent to the existence of the adjoint of A

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10.1002/malq.19990450205

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References found in this work

Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
Foundations of Constructive Analysis.John Myhill - 1972 - Journal of Symbolic Logic 37 (4):744-747.
Varieties of constructive mathematics.D. S. Bridges & Fred Richman - 1987 - New York: Cambridge University Press. Edited by Fred Richman.
Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Continuity and nondiscontinuity in constructive mathematics.Hajime Ishihara - 1991 - Journal of Symbolic Logic 56 (4):1349-1354.

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