## Linear Operators: General theory |

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Page 151

llo lim sup [ { SF , 1tu ( s ) –t ( s ) [ po ( ya , ds ) } \\ ” + { / folkm ( s ) – f ( s ) [ Þv ( u ,

ds ) !!! ] + 2ello m , n - 00 m , n - 00 m , n - 00 281 / P , so that lim In - Imlı = 0.

**Consequently**, lim sup \ tu — imlı Slim sup { St. \ n ( s ) – Im ( s [ pd ( u , ds ) " " + 2llo lim sup [ { SF , 1tu ( s ) –t ( s ) [ po ( ya , ds ) } \\ ” + { / folkm ( s ) – f ( s ) [ Þv ( u ,

ds ) !!! ] + 2ello m , n - 00 m , n - 00 m , n - 00 281 / P , so that lim In - Imlı = 0.

Page 254

This shows that for arbitrary a 0 = ( Ux , ÂUy ) + ( Ux , 2Uy ) , and if we let à = ( Ux

, Uy ) in this equation it is seen that ( Ux , Uy ) 0. Thus U maps an orthonormal

basis for H , onto an orthonormal basis for H2 , and

...

This shows that for arbitrary a 0 = ( Ux , ÂUy ) + ( Ux , 2Uy ) , and if we let à = ( Ux

, Uy ) in this equation it is seen that ( Ux , Uy ) 0. Thus U maps an orthonormal

basis for H , onto an orthonormal basis for H2 , and

**consequently**V , and H , have...

Page 637

Nelson Dunford, Jacob T. Schwartz, William G. Bade. which proves ( iii ) and ( v )

for the case n = m + 1 .

n . We now obtain an estimate for the series monoxin ) ( t ) which majorizes noo ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. which proves ( iii ) and ( v )

for the case n = m + 1 .

**Consequently**, ( i ) , . . . , ( v ) are proved inductively for alln . We now obtain an estimate for the series monoxin ) ( t ) which majorizes noo ...

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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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