## Linear Operators: Spectral theory |

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Page 1064

But it is

But it is

**clear**that gm ( x ) = g ( x ) for all x . Hence q = g , proving that g , 54,111 , if f is in CŪ ( 1 ) and vanishes outside a bounded set . Next let s be in L , ( E " ) , and let { { m } be a sequence of functions in Co ( E " ) ...Page 1196

lim ( T ) x , X e D ( ( T ) ) . n It is

lim ( T ) x , X e D ( ( T ) ) . n It is

**clear**from Theorem 3 that if | ( 2 ) = a then f ( T ) T but it is not**clear**that if f is the polynomial do tayat ... tana " then ( T ) is the polynomial QoI + a , T + ...Page 1689

Indeed , if { { m } is a Cauchy sequence in L ( 1 ) , it is

Indeed , if { { m } is a Cauchy sequence in L ( 1 ) , it is

**clear**from ( i ) that { a { m } is a Cauchy sequence in L , ( I ) for IJI S k , so that there exist functions g , g ) in L , ( I ) such that limm - com - gj , = 0 and limm ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero