## Linear Operators, Part 2 |

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Page 1175

Then K 1 is a bounded

each real $ o , let H . be the

H1 ) ( 5 ) = f ( s ) , > 60 , = 0 otherwise . By Corollary 22 , it follows that there is a ...

Then K 1 is a bounded

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

**mapping**in La ( L ( S ) ) defined by the formula ( 47 ) (H1 ) ( 5 ) = f ( s ) , > 60 , = 0 otherwise . By Corollary 22 , it follows that there is a ...

Page 1401

j - dimensional subspace S , of Dt , and let D ; be its orthocomplement in Dt .

Define an isometric

x = - Ux , Let l ' ; be the graph of U ; : By Theorem XII . 4 . 12 ( b ) , D ( T . ) OT ; is

the ...

j - dimensional subspace S , of Dt , and let D ; be its orthocomplement in Dt .

Define an isometric

**mapping**U , of Dt onto D _ as follows : U ; æ = Ux , XES ; , U ;x = - Ux , Let l ' ; be the graph of U ; : By Theorem XII . 4 . 12 ( b ) , D ( T . ) OT ; is

the ...

Page 1734

Let U , C1 , be a bounded neighborhood of q chosen so small that BU , CE , and

so that there exists a

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

Let U , C1 , 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 ) q is one - to - one , is infinitely often differentiable , and y ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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