## Linear Operators: Spectral theory |

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Page 861

In this connection it is desirable to note that an element T. et(3) has an inverse as

an element of B(3) if and only if a has an inverse in 3 and that when this inverse T

.”

In this connection it is desirable to note that an element T. et(3) has an inverse as

an element of B(3) if and only if a has an inverse in 3 and that when this inverse T

.”

**exists**, then T.” = T-1. Clearly if a-1**exists**then T-1T = T, T-1 = I. If T.'**exists**in ...Page 1057

provided only that the limit in the braces in this last equation

complete the proof of the present lemma, it suffices to show that Q Q (3) 6(u) = %

o e” dy= lim s o e” dy e” ly ;:.." esswish |y|

integral ...

provided only that the limit in the braces in this last equation

**exists**. Thus, tocomplete the proof of the present lemma, it suffices to show that Q Q (3) 6(u) = %

o e” dy= lim s o e” dy e” ly ;:.." esswish |y|

**exists**for each u. By Lemma 2, theintegral ...

Page 1261

23 If an operator T has a closed linear extension there

linear extension T such that if T is any closed linear extension of T then TC T1. T

is called the closure of T. (a) There

closed ...

23 If an operator T has a closed linear extension there

**exists**a unique closedlinear extension T such that if T is any closed linear extension of T then TC T1. T

is called the closure of T. (a) There

**exists**a densely defined operator with noclosed ...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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