## Linear Operators: General theory |

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Page 20

Thus A , + X , and Al is open , and

< 1 / 2 . By assumption , the set A2 does not

hence the non - void open set Aan S ( Pı , & z / 2 )

Thus A , + X , and Al is open , and

**contains**a sphere S , = S ( P1 , & i ) with 0 < & i< 1 / 2 . By assumption , the set A2 does not

**contain**the open set S ( P1 , & 1 / 2 ) ;hence the non - void open set Aan S ( Pı , & z / 2 )

**contains**a sphere S , = S ...Page 56

of the image of any neighborhood G of the element 0 in X

neighborhood of the element 0 in Y . Since a - b is a continuous function of a and

b , there is a neighborhood M of 0 such that M - MCG . For every x e X , æ / n + 0 ,

and so x e ...

of the image of any neighborhood G of the element 0 in X

**contains**aneighborhood of the element 0 in Y . Since a - b is a continuous function of a and

b , there is a neighborhood M of 0 such that M - MCG . For every x e X , æ / n + 0 ,

and so x e ...

Page 309

The set A = S - U E ; then

will now be shown that every measurable subset B of A

u ( F ) < € . Suppose , on the contrary , that some such set B

with ...

The set A = S - U E ; then

**contains**no atoms having measure greater than ε . Itwill now be shown that every measurable subset B of A

**contains**a set F with 0 <u ( F ) < € . Suppose , on the contrary , that some such set B

**contains**no set ofwith ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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