## Linear Operators, Part 1 |

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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 ( 2 – 3 arti ! 0 . n n -

00 8 Let ( wn } be a

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

**basis**for X if to each xe X therecorresponds a unique sequence { Q } of scalars such that lim ( 2 – 3 arti ! 0 . n n -

00 8 Let ( wn } be a

**basis**in the F - space X , and let y be the vector space of all ...Page 254

The cardinality of an arbitrary orthonormal

dimension . 16 THEOREM . Two Hilbert spaces are isometrically isomorphic if

and only if they have the same dimension . Proof . Let U be an isometric

isomorphism of ...

The cardinality of an arbitrary orthonormal

**basis**of a Hilbert space H is itsdimension . 16 THEOREM . Two Hilbert spaces are isometrically isomorphic if

and only if they have the same dimension . Proof . Let U be an isometric

isomorphism of ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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