Derivations on algebras of unbounded operators

Inoue, Atsushi; Ota, Shôichi

doi:10.1090/S0002-9947-1980-0580903-X

Derivations on algebras of unbounded operators
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by Atsushi Inoue and Shôichi Ota

Trans. Amer. Math. Soc. 261 (1980), 567-577

DOI: https://doi.org/10.1090/S0002-9947-1980-0580903-X

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Abstract:

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general *-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left $E{W^\# }$-algebra induced by an unbounded Hilbert algebra is strongly implemented by an operator which belongs to an algebra of measurable operators.

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algebras and

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Recent developments in the theory of unbounded derivations in

algebras

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