## Linear Operators: Spectral theory |

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Page 1175

Then X , is a bounded

each real & o , let H to be the

) ( H1 ) ( 5 ) = f ( 5 ) , & > 50 otherwise . = 0 By Corollary 22 , it follows that there ...

Then X , is a bounded

**mapping**of the space L , ( L , ( S ) ) into itself . . Proof . Foreach real & o , let H to be the

**mapping**in L , ( L , ( S ) ) defined by the formula ( 47) ( H1 ) ( 5 ) = f ( 5 ) , & > 50 otherwise . = 0 By Corollary 22 , it follows that there ...

Page 1401

Nelson Dunford, Jacob T. Schwartz. j - dimensional subspace S , of Dt , and let O

, be its orthocomplement in D . Define an isometric

follows : + U ; x Ux , X e Sj , U , x -Ur , αε , . Let I , be the graph of Uj : By Theorem

...

Nelson Dunford, Jacob T. Schwartz. j - dimensional subspace S , of Dt , and let O

, be its orthocomplement in D . Define an isometric

**mapping**U , of Dt onto D asfollows : + U ; x Ux , X e Sj , U , x -Ur , αε , . Let I , be the graph of Uj : By Theorem

...

Page 1734

Let U , CT , be a bounded neighborhood of q chosen so small that BU , CE , and

so that there exists a

the origin such that ( i ) y is one - to - one , is infinitely often differentiable , and o ...

Let U , CT , be a bounded neighborhood of q chosen so small that BU , CE , and

so that there exists a

**mapping**o of U , onto the unit spherical neighborhood V ofthe origin such that ( i ) y is one - to - one , is infinitely often differentiable , and o ...

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