## Linear Operators: General theory |

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Page 88

.x = p ( x ) + p ( -x ) , then this

separability

the Hahn - Banach theorem to hold when the field of scalars is non ...

.x = p ( x ) + p ( -x ) , then this

**condition**is sufficient . Bonsall [ 1 ] showed that theseparability

**condition**cannot be dropped . Ingleton ( 1 ) has given**conditions**forthe Hahn - Banach theorem to hold when the field of scalars is non ...

Page 131

To prove the sufficiency of the

satisfies this

and imaginary parts satisfy the same

is ...

To prove the sufficiency of the

**condition**we observe first that a set function àsatisfies this

**condition**if and only if the positive and negative variations of its realand imaginary parts satisfy the same

**condition**. Thus , it may be assumed that ais ...

Page 487

in S. Hence , by IV.6.6 , the

an equicontinuous subset of C ( S * ) . It follows from Theorem IV.6.7 , that T ( S )

is conditionally compact in the metric of Y if and only if the

in S. Hence , by IV.6.6 , the

**condition**is equivalent to the statement that T ( S ) isan equicontinuous subset of C ( S * ) . It follows from Theorem IV.6.7 , that T ( S )

is conditionally compact in the metric of Y if and only if the

**condition**is satisfied .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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