## Linear Operators, Part 2 |

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Page 928

Mimura [ 1 ] simplified Riesz ' s proof , and

operators . A more elementary proof was given by Sz . - Nagy [ 3 ; pp . 63 - 65 ] (

see also Riesz and Sz . - Nagy [ 1 ; Sec . 129 ] , Nakano [ 8 , 9 ] and Wecken [ 2 ] )

.

Mimura [ 1 ] simplified Riesz ' s proof , and

**extended**the result to unboundedoperators . A more elementary proof was given by Sz . - Nagy [ 3 ; pp . 63 - 65 ] (

see also Riesz and Sz . - Nagy [ 1 ; Sec . 129 ] , Nakano [ 8 , 9 ] and Wecken [ 2 ] )

.

Page 1165

It is well known that , by applying standard inequalities to functions with values in

an appropriate Banach space , the applicability of these inequalities can often be

usefully

It is well known that , by applying standard inequalities to functions with values in

an appropriate Banach space , the applicability of these inequalities can often be

usefully

**extended**. For this reason , it is noteworthy that , whereas M . Riesz ...Page 1379

Then if , for ; > k , the functions 0 ; ; ( ) of Theorem 18 ( or , the functions 07 ; ( 2 ) of

Theorem 18 ) may be

neighborhood U of 1 , 01 , . . . , 0x is a determining set for T . PROOF . If 07 ( • ) is

...

Then if , for ; > k , the functions 0 ; ; ( ) of Theorem 18 ( or , the functions 07 ; ( 2 ) of

Theorem 18 ) may be

**extended**to analytic functions defined on the wholeneighborhood U of 1 , 01 , . . . , 0x is a determining set for T . PROOF . If 07 ( • ) is

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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