## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2214

5 , the

strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves invariant ...

5 , the

**weakly**closed operator algebra W ( B ) generated by B is the same as thestrongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves invariant ...

Page 2217

A bounded linear operator is in the

a o - complete Boolean algebra B of projections in a B - space if and only if it

leaves invariant every closed linear manifold which remains invariant under

every ...

A bounded linear operator is in the

**weakly**closed operator algebra generated bya o - complete Boolean algebra B of projections in a B - space if and only if it

leaves invariant every closed linear manifold which remains invariant under

every ...

Page 2218

as the

uniformly closed operator algebra generated by B . Every operator in such a

uniformly closed algebra is , by Lemma 9 , given in terms of a countably additive

spectral ...

as the

**weakly**closed operator algebra generated by B ) is the same as theuniformly closed operator algebra generated by B . Every operator in such a

uniformly closed algebra is , by Lemma 9 , given in terms of a countably additive

spectral ...

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