A transitivity theorem for algebras of elementary operators

Author:
Bojan Magajna

Journal:
Proc. Amer. Math. Soc. **118** (1993), 119-127

MSC:
Primary 46L05; Secondary 47B48, 47D25

DOI:
https://doi.org/10.1090/S0002-9939-1993-1158004-6

MathSciNet review:
1158004

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Abstract: Let be a -algebra and the algebra of all elementary operators on , and let . It is proved that is contained in the closure of the set if and only if each complex linear combination is contained in the closed two-sided ideal generated by . In particular, a bounded linear operator on preserves all closed two-sided ideals if and only if it is in the strong closure of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1158004-6

Keywords:
Elementary operators,
-algebra,
von Neumann algebra

Article copyright:
© Copyright 1993
American Mathematical Society