✦ LIBER ✦

Weak-operator Continuity and the Existence of Adjoints

✍ Scribed by Douglas Bridges; Luminita Dediu

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 237 KB
Volume: 45
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19990450205

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✦ Synopsis

Abstract

It is shown, within constructive mathematics, that the unit ball B~1~(H) 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 B~1~(H) is equivalent to the existence of the adjoint of A.

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