Geodesic
Trace-Class Operators in CSL Algebras
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 416-422

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In this note we show that if L is a commutative subspace lattice, then every trace-class operator in Alg L lies in the norm-closure of the span of rank-one operators in Alg L. We also give an elementary proof of a recent result of Davidson and Pitts that if L is a CSL generated by completely distributive lattice and finitely many commuting chains, then L is compact in the strong operator topology if and only if L is completely distributive.
DOI : 10.4153/CMB-1992-055-x
Mots-clés : 47D25, 46L10 
Rosenoer, Shlomo. Trace-Class Operators in CSL Algebras. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 416-422. doi: 10.4153/CMB-1992-055-x
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     title = {Trace-Class {Operators} in {CSL} {Algebras}},
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     year = {1992},
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     doi = {10.4153/CMB-1992-055-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-055-x/}
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