## Linear Operators: Spectral theory |

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Page 970

Hence , by Theorem 9 , tf is the

sequence { t ( x.f ) } . Equivalently , we write tf lim s [ x , : ] / ( x ) ... We now show

that the function f can be retrieved from tf by a similar

THEOREM .

Hence , by Theorem 9 , tf is the

**limit**in the norm of L ( M ) of the generalizedsequence { t ( x.f ) } . Equivalently , we write tf lim s [ x , : ] / ( x ) ... We now show

that the function f can be retrieved from tf by a similar

**limiting**procedure . 16THEOREM .

Page 1124

If E ,, E are in F and q ( En ) increases to the

we have already proved that E is an increasing sequence of projections and E ,

SE . If Ec is the strong

...

If E ,, E are in F and q ( En ) increases to the

**limit**9 ( E ) , then it follows from whatwe have already proved that E is an increasing sequence of projections and E ,

SE . If Ec is the strong

**limit**of En , then E. SE and Q ( E ) = Q ( E ) . Thus , it follows...

Page 1129

1 sn sm . m Thus E ( e ) is the strong

, it follows from Theorem X.2.1 that Om belongs to the algebra A , so that one is a

1 sn sm . m Thus E ( e ) is the strong

**limit**of the operators Om . On the other hand, it follows from Theorem X.2.1 that Om belongs to the algebra A , so that one is a

**limit**of linear combinations of products of the operators E. Since the projections ...### What people are saying - Write a review

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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