Weak‐operator Continuity and the Existence of Adjoints | Zendy

Bridges Douglas | Zendy; Dediu Luminita | Zendy

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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

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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