## Linear Operators: Spectral theory |

### From inside the book

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Page 884

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the

here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this

...

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the

**results**given in Section 1 are due . ... The proof of this lemma givenhere is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this

**result**in...

Page 928

Mimura [ 1 ] simplified Riesz ' s proof , and extended the

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 1419

Clearly , f has a single minimum f ( mi + 1 ) between 8i + 1 and Si + 2 , a single

maximum f ( mi + 2 ) between Si + 2 and sits , etc . We will show that \ / ( m : ) 2 \ | (

Mi + 1 ) 1 2 \ | ( mi + 2 ) | 2 . . . , which will clearly establish the desired

Clearly , f has a single minimum f ( mi + 1 ) between 8i + 1 and Si + 2 , a single

maximum f ( mi + 2 ) between Si + 2 and sits , etc . We will show that \ / ( m : ) 2 \ | (

Mi + 1 ) 1 2 \ | ( mi + 2 ) | 2 . . . , which will clearly establish the desired

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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