## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2044

On the real axis 0 = 0 and hence , since T ' ( t ) is

) | T ( ) SK , Ost < 00 , a fact which also follows from ( 61 ) . The inequality ( 81 )

shows that T ( 5 ) is

On the real axis 0 = 0 and hence , since T ' ( t ) is

**strongly**continuous at t = 0 , ( 82) | T ( ) SK , Ost < 00 , a fact which also follows from ( 61 ) . The inequality ( 81 )

shows that T ( 5 ) is

**strongly**continuous at $ = 0 provided & remains in a sector ...Page 2194

attempt will be made to characterize the strong closure of a commutative algebra

of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the

...

**Strongly**Closed Algebras and Complete Boolean Algebras In this section anattempt will be made to characterize the strong closure of a commutative algebra

of spectral operators . It has been observed ( cf . VI . 1 . 5 ) that a convex set in the

...

Page 2220

Thus , since the product of bounded ,

sequences is itself a

Ta ) + f ( T )

4M sup ...

Thus , since the product of bounded ,

**strongly**convergent generalizedsequences is itself a

**strongly**convergent generalized sequence , we see that r (Ta ) + f ( T )

**strongly**. Now , from Theorem 2 . 10 , Ir ( Tm ) ] = [ " ( A ) E _ ( da ) | S4M sup ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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