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Weak‐operator Continuity and the Existence of Adjoints
Author(s) -
Bridges Douglas,
Dediu Luminita
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450205
Subject(s) - mathematics , bounded function , bounded operator , hilbert space , weak operator topology , operator (biology) , quasinormal operator , constructive , unit sphere , finite rank operator , operator space , pure mathematics , ball (mathematics) , hermitian adjoint , compact operator , discrete mathematics , mathematical analysis , banach space , process (computing) , computer science , biochemistry , extension (predicate logic) , gene , programming language , operating system , chemistry , repressor , transcription factor
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.