## Linear Operators: General theory |

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Page 36

The cardinality of a Hamel

is called the dimension of the linear space . This independence is readily proved

if there is a finite Hamel

The cardinality of a Hamel

**basis**is a number independent of the Hamel**basis**; itis called the dimension of the linear space . This independence is readily proved

if there is a finite Hamel

**basis**, in which case the space is said to be finite ...Page 71

A sequence { xn } in an F - space X is called a

corresponds a unique sequence { Q ; } of scalars such that lim ( w – gaixil = 0 . n

+ i = 1 8 Let { xn } be a

all ...

A sequence { xn } in an F - space X is called a

**basis**for X if to each x € X therecorresponds a unique sequence { Q ; } of scalars such that lim ( w – gaixil = 0 . n

+ i = 1 8 Let { xn } be a

**basis**in the F - space X , and let y be the vector space ofall ...

Page 254

Thus by forming the chain VR , U « » . . . , Ume ' s Up . it is seen that vp is

equivalent to Vg , and thus that Vg is in V . Since { vs } is a

has an expansion of the form ug = £6 ( Uq , v ) Og , so that ug is in the closed

linear ...

Thus by forming the chain VR , U « » . . . , Ume ' s Up . it is seen that vp is

equivalent to Vg , and thus that Vg is in V . Since { vs } is a

**basis**, the vector u ,has an expansion of the form ug = £6 ( Uq , v ) Og , so that ug is in the closed

linear ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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