## 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

If the range of T, properly

space, R(T,)

element y such that 0 # Toye 92. But this is impossible, since if Toye 9t, then

since T.

If the range of T, properly

**contains**the range of T1, then, since R(T,) is a linearspace, R(T,)

**contains**an element orthogonal to Št(T1). Thus 3)(T,)**contains**anelement y such that 0 # Toye 92. But this is impossible, since if Toye 9t, then

since T.

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

38 other sections not shown

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