## Linear Operators: Spectral theory |

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Page 995

If p and f are in Lee (R) and L1(R) respectively and if f(m) = 0 for every m in the

spectral set atop), then g(fo p)

with h(mo) = 1 and h vanishing on an open set

p).

If p and f are in Lee (R) and L1(R) respectively and if f(m) = 0 for every m in the

spectral set atop), then g(fo p)

**contains**no isolated points. ... Let h be in L1(R)with h(mo) = 1 and h vanishing on an open set

**containing**the remainder of a (f 4p).

Page 996

Since f * p is continuous by Lemma 3.1(d) it follows from the above equation that f

* p # 0. From Lemma 12(b) it is seen that g(fo p) Co.(p) and from Lemma 12(c)

and the equation of =7; it follows that or( f * p)

Since f * p is continuous by Lemma 3.1(d) it follows from the above equation that f

* p # 0. From Lemma 12(b) it is seen that g(fo p) Co.(p) and from Lemma 12(c)

and the equation of =7; it follows that or( f * p)

**contains**no interior point of a (p).Page 1397

Thus 3)(T,)

since if Toye 9t, then since T. DTI and T192 = 0, it follows that (Tay, Tay) = (T.Toy,

y) = 0, and therefore that Toy = 0. Thus Şt(T,) = $st(T1); XIII.6.7 QUALITATIVE ...

Thus 3)(T,)

**contains**an element y such that 0 # Toye 92. But this is impossible,since if Toye 9t, then since T. DTI and T192 = 0, it follows that (Tay, Tay) = (T.Toy,

y) = 0, and therefore that Toy = 0. Thus Şt(T,) = $st(T1); XIII.6.7 QUALITATIVE ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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