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

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Page 1936

+ En where E1 , . . . , En are bounded , disjoint projections in X , each commuting

with the bounded operator T . Then T is a spectral operator if and only if each

+ En where E1 , . . . , En are bounded , disjoint projections in X , each commuting

with the bounded operator T . Then T is a spectral operator if and only if each

**restriction**T | E , X is a spectral operator . If T is a spectral operator , then the ...Page 2094

( X ) is reduced by a closed subspace Y = X and one of its complements ( that is ,

if T commutes with some projection of X onto Y ) , then the

**Restrictions**and quotients . Theorem 3 . 10 shows that if a spectral operator Te B( X ) is reduced by a closed subspace Y = X and one of its complements ( that is ,

if T commutes with some projection of X onto Y ) , then the

**restriction**T | Y of T to ...Page 2228

If o is a Borel set , and T is a spectral operator with resolution of the identity E ,

then the

resolution of the identity is the

) X is ...

If o is a Borel set , and T is a spectral operator with resolution of the identity E ,

then the

**restriction**T | E ( 0 ) X of T to E ( 0 ) X is a spectral operator whoseresolution of the identity is the

**restriction**of E to E ( 0 ) X . If o is bounded , T | E ( 0) X is ...

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