## Linear Operators: General theory |

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Page 253

An equivalence class U of vectors wą will be said to

equivalence class V of vectors if there is a pair of vectors , one from U and one

from V ... Suppose that U and V are

Ua EU .

An equivalence class U of vectors wą will be said to

**correspond**to anequivalence class V of vectors if there is a pair of vectors , one from U and one

from V ... Suppose that U and V are

**corresponding**equivalence classes and thatUa EU .

Page 254

It is thus seen that

same closed linear manifold M. Hence , if one of U and V is finite , M is finite

dimensional , and therefore the other of U and V is finite and has the same

cardinality .

It is thus seen that

**corresponding**equivalence classes U and V determine thesame closed linear manifold M. Hence , if one of U and V is finite , M is finite

dimensional , and therefore the other of U and V is finite and has the same

cardinality .

Page 720

Establish the

group of operators . Show that the convergence almost everywhere in Theorem

6.9 remains valid if ( S , E , u ) is a finite measure space and Ss \ | ( s ) / ( 1+ log +

...

Establish the

**corresponding**results for a strongly measurable nparameter semi -group of operators . Show that the convergence almost everywhere in Theorem

6.9 remains valid if ( S , E , u ) is a finite measure space and Ss \ | ( s ) / ( 1+ log +

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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