## Linear Operators: Spectral operators |

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Page 1936

If T is a spectral operator , then the resolution of the identity for the

; X is the corresponding

Let T be a spectral operator . By Corollary 7 , E ¡ commutes with every ...

If T is a spectral operator , then the resolution of the identity for the

**restriction**T | E; X is the corresponding

**restriction**of the resolution of the identity for T . PROOF .Let T be a spectral operator . By Corollary 7 , E ¡ commutes with every ...

Page 2094

( X ) is reduced by a closed subspace Y SX 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 SX 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 ( o ) 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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