## Linear Operators: General theory |

### From inside the book

Results 1-3 of 79

Page 598

Suppose that gn ( T ) converges in the

operator . Let € 0 ( T ) , and limn - 8n ( 2 ) + 0 . Show that 2 is a pole of o ( T ) , and

that E ( 2 ; T ) X has a positive finite dimension . ( Hint . See Exercise VII . 5 . 35 . )

...

Suppose that gn ( T ) converges in the

**uniform**operator topology to a compactoperator . Let € 0 ( T ) , and limn - 8n ( 2 ) + 0 . Show that 2 is a pole of o ( T ) , and

that E ( 2 ; T ) X has a positive finite dimension . ( Hint . See Exercise VII . 5 . 35 . )

...

Page 841

17 ( 23 ) representation as a C - space , almost periodic functions , IV . 7 . 6 ( 285

) bounded functions , IV . 6 . 18 - 22 ( 274 – 277 ) special C - spaces , ( 397 – 398

)

17 ( 23 ) representation as a C - space , almost periodic functions , IV . 7 . 6 ( 285

) bounded functions , IV . 6 . 18 - 22 ( 274 – 277 ) special C - spaces , ( 397 – 398

)

**uniform**continuity , 1 . 6 . 16 – 18 ( 23 – 24 ) of almost periodic functions , IV .Page 857

5 ( 32 ) remarks on , ( 730 )

properties , VI . 9 . 11 - 12 ( 512 - 513 ) Unit , of a group , ( 34 ) Unit sphere in a

normed space , compactness and finite dimensionality of , IV . 3 . 5 ( 245 ) ...

5 ( 32 ) remarks on , ( 730 )

**Uniform**operator topology , definition , VI . 1 . 1 ( 475 )properties , VI . 9 . 11 - 12 ( 512 - 513 ) Unit , of a group , ( 34 ) Unit sphere in a

normed space , compactness and finite dimensionality of , IV . 3 . 5 ( 245 ) ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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