Geodesic
On Reflexivity of Algebras
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1291-1308

Voir la notice de l'article provenant de la source Cambridge University Press

For each natural number n we define to be the class of all weakly closed algebras of (bounded linear) operators on a separable Hilbert space H such that the lattice of invariant subspaces of and (alg lat )(n) are the same. (If A is an operator, A (n) denotes the direct sum of n copies of A; if is a collection of operators,. Also, alg lat denotes the algebra of all operators leaving all invariant subspaces of invariant.) In the first section we show that . In Section 2 we prove that every weakly closed algebra containing a maximal abelian self adjoint algebra (m.a.s.a.) is , and that . It is also shown that certain algebras containing a m.a.s.a. are necessarily reflexive. 
Radjabalipour, Mehdi. On Reflexivity of Algebras. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1291-1308. doi: 10.4153/CJM-1981-098-5
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