## Linear operators: Spectral operators |

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Page 2152

To

<r(a;)ES}. It will be shown that 9Jt(8) is closed. For every x we have a{x) e a(T) e

ro and thus 2Jl(8) = 9Jl(8F0), which allows us to assume, with no loss of ...

To

**prove**(C), let 8 be a closed subset of the complex plane and let W(8)={x\xeX,<r(a;)ES}. It will be shown that 9Jt(8) is closed. For every x we have a{x) e a(T) e

ro and thus 2Jl(8) = 9Jl(8F0), which allows us to assume, with no loss of ...

Page 2236

This

and let {en} be as above. Then, since T \ E(en)X is bounded, statements (i) and (ii

) and the functional calculus of bounded operators (cf. VII. 3. 10) may be applied

...

This

**proves**(iii). The proof of (viii) is evident. To**prove**(vi), lets be in t)(f(T) + g(T))and let {en} be as above. Then, since T \ E(en)X is bounded, statements (i) and (ii

) and the functional calculus of bounded operators (cf. VII. 3. 10) may be applied

...

Page 2459

If x„ e ]Tac (H) and limn^x xn =x, then, by what we have already

write x = yx + y2 + «/3 , where yx e Łac (H) and y2 , y3 are orthogonal to Łac (H).

... Using this last fact, it is easy to

If x„ e ]Tac (H) and limn^x xn =x, then, by what we have already

**proved**, we maywrite x = yx + y2 + «/3 , where yx e Łac (H) and y2 , y3 are orthogonal to Łac (H).

... Using this last fact, it is easy to

**prove**assertion (c) of the present lemma.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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