## Linear Operators: General theory |

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Page 114

integrable simple functions ; to prove it in the general case , let ' n be a sequence

of finitely valued M - simple functions which determine g . Then the functions T / n

...

**Statement**( b ) is clear from the definitions .**Statement**( c ) is evident for u -integrable simple functions ; to prove it in the general case , let ' n be a sequence

of finitely valued M - simple functions which determine g . Then the functions T / n

...

Page 415

If X is a linear topological space , then ( ii ) co ( A ) = co ( A ) , ( iii ) co ( A ) = a CO

( A ) , ( iv ) If CO ( A ) is compact , then co ( A + B ) = CO ( A ) + co ( B ) . PROOF .

The first part of

If X is a linear topological space , then ( ii ) co ( A ) = co ( A ) , ( iii ) co ( A ) = a CO

( A ) , ( iv ) If CO ( A ) is compact , then co ( A + B ) = CO ( A ) + co ( B ) . PROOF .

The first part of

**statement**( i ) follows in an elementary fashion from Lemma 1.4 .Page 447

+ ayz ) .

y ) + 7 ( x , y ) = T ( x , 0 ) = ( ) •T ( x , y ) = 0 .

**Statement**( b ) follows from the inequality 2 + ( x + = ( 4x + y2 ) ) = f ( x + ayı ) + ( x+ ayz ) .

**Statement**( c ) is trivial .**Statement**( d ) follows from the inequality t ( x , -y ) + 7 ( x , y ) = T ( x , 0 ) = ( ) •T ( x , y ) = 0 .

**Statement**( e ) is trivial . Q . E . D . 4 ...### What people are saying - Write a review

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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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