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On Reflexivity of Algebras

Published online by Cambridge University Press:  20 November 2018

Mehdi Radjabalipour
Mehdi Radjabalipour*
Affiliation:
University of Mazandaran, Babolsar, Iran
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 6 , 01 December 1981 , pp. 1291 - 1308
Copyright
Copyright © Canadian Mathematical Society 1981

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