## Linear Operators: Spectral theory |

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Page 1662

Then the closed set Cp in I , which is the complement of the largest open set in I

in which F vanishes , i.e. , which is the complement in I of the union of all the

open

may ...

Then the closed set Cp in I , which is the complement of the largest open set in I

in which F vanishes , i.e. , which is the complement in I of the union of all the

open

**subsets**of I in which F vanishes , is called the carrier of F. Lemma 12 nowmay ...

Page 1663

Nelson Dunford, Jacob T. Schwartz. that F1 , is in ( 1. ) for each open

whose closure is compact and contained in I. 35 DEFINITION . Let I be an open

...

Nelson Dunford, Jacob T. Schwartz. that F1 , is in ( 1. ) for each open

**subset**I. of Iwhose closure is compact and contained in I. 35 DEFINITION . Let I be an open

**subset**of C and let k be a positive integer . ( i ) The set of all F in D ( 1 ) for which...

Page 1696

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has

a carrier which is a compact

Hence , we can evidently suppose without loss of generality that the carrier C of F

is ...

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has

a carrier which is a compact

**subset**Cm of I , and such that F , → F as m + 00.Hence , we can evidently suppose without loss of generality that the carrier C of F

is ...

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