## Linear Operators: Spectral theory |

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Page 952

If i Sp < 0 , it is readily seen from Corollary III.3.8 and the regularity of 2 that the

collection of functions which are

is dense in L ( R ) . Hence for f in L , ( R ) let k be such a

14 ...

If i Sp < 0 , it is readily seen from Corollary III.3.8 and the regularity of 2 that the

collection of functions which are

**continuous**and vanish outside of compact setsis dense in L ( R ) . Hence for f in L , ( R ) let k be such a

**continuous**function with14 ...

Page 968

PROOF . Verification that the neighborhoods N ( h , K , € ) are a base for a

topology will be left to the reader . If heN ( h , K , e ) and hq E N ( ho , K , ε ) then

hy h , E N ( hho , K2 , ε ) so that multiplication is

then hi ...

PROOF . Verification that the neighborhoods N ( h , K , € ) are a base for a

topology will be left to the reader . If heN ( h , K , e ) and hq E N ( ho , K , ε ) then

hy h , E N ( hho , K2 , ε ) so that multiplication is

**continuous**. If hy e N ( h , K , ε )then hi ...

Page 1903

( See also Absolutely

, IV.15 definition , IV.2.14 ( 240 ) remarks concerning , ( 373-386 ) study of , IV.6

characterizations of C - space , ( 396397 ) on a compact space , 1.5.8 ( 18 ) ...

( See also Absolutely

**continuous**functions ) as a B - space , additional properties, IV.15 definition , IV.2.14 ( 240 ) remarks concerning , ( 373-386 ) study of , IV.6

characterizations of C - space , ( 396397 ) on a compact space , 1.5.8 ( 18 ) ...

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