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

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Page 2094

The situation corresponding to an

. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

The situation corresponding to an

**invariant**closed subspace of T is not so simple. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

**invariant**closed subspace y of X is spectral if and only if the resolution of the ...Page 2214

5 , the weakly closed operator algebra W ( B ) generated by B is the same as 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

5 , the weakly closed operator algebra W ( B ) generated by B is the same as 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**...Page 2286

... between the subspaces of X

, the resolution of the identity of Q . 37 DEFINITION . If M is a closed

subspace in X , we denote by ( M ) the closure in H of the linear set A ( M D ( A ) )

.

... between the subspaces of X

**invariant**under B and those of H**invariant**under B, the resolution of the identity of Q . 37 DEFINITION . If M is a closed

**invariant**subspace in X , we denote by ( M ) the closure in H of the linear set A ( M D ( A ) )

.

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