## Linear Operators, Part 1 |

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Results 1-3 of 18

Page 566

Nevertheless , the procedure suggested by Theorem 1.10 will enable us to

generalize many of the results of Section 1 to the infinite dimensional case . We

begin by studying the function ( 21 - T ) -1 , DEFINITION . The

of T is ...

Nevertheless , the procedure suggested by Theorem 1.10 will enable us to

generalize many of the results of Section 1 to the infinite dimensional case . We

begin by studying the function ( 21 - T ) -1 , DEFINITION . The

**resolvent**set o ( T )of T is ...

Page 591

... in the

function f of Theorem 10 is analytic on a neighborhood of ( S + N ) as stated .

Now let C denote the union of a finite collection C1 , ... , Cn of disjoint closed

rectifiable ...

... in the

**resolvent**set of S + N and R ( 2 ; S + N ) = R ( 2 ; S ) " + 1N " . Thus thefunction f of Theorem 10 is analytic on a neighborhood of ( S + N ) as stated .

Now let C denote the union of a finite collection C1 , ... , Cn of disjoint closed

rectifiable ...

Page 607

54 , 2 ] had obtained expansions for the

neighborhood of a pole . A special case of Theorem 1.9 is due to Weyr [ 1 ] , and

in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1.10 ,

Frobenius ( 3 ; p .

54 , 2 ] had obtained expansions for the

**resolvent**( 21 –T ) -1 in theneighborhood of a pole . A special case of Theorem 1.9 is due to Weyr [ 1 ] , and

in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1.10 ,

Frobenius ( 3 ; p .

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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