## Linear Operators: Spectral operators |

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and the fraction in the

bounded on all of R". Thus A9 has a resolution of the identity. Furthermore, the

set <ZX is the null set {s | sx = «2 = 0}, so that A§ is a scalar type operator to

which ...

and the fraction in the

**inequality**(i) of Theorem 6 is \s2x-sl\2 + 2\s1s2\2 which isbounded on all of R". Thus A9 has a resolution of the identity. Furthermore, the

set <ZX is the null set {s | sx = «2 = 0}, so that A§ is a scalar type operator to

which ...

Page 2190

From the preceding lemma it is seen that the map /->&(/) is a continuous

homomorphism of EB(A, E) onto an algebra of scalar type spectral operators.

Thus for some constant K we have \S(f)\ ^ K \f\ and to prove the final

the present ...

From the preceding lemma it is seen that the map /->&(/) is a continuous

homomorphism of EB(A, E) onto an algebra of scalar type spectral operators.

Thus for some constant K we have \S(f)\ ^ K \f\ and to prove the final

**inequality**ofthe present ...

Page 2399

The

42b) may be deduced in a precisely similar way, the proof of our theorem is now

complete. Q.E.D. We conclude the present section with an additional remark ...

The

**inequality**(42a) follows immediately from (43) and (45). Since the**inequality**(42b) may be deduced in a precisely similar way, the proof of our theorem is now

complete. Q.E.D. We conclude the present section with an additional remark ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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