## Linear Operators: Spectral theory |

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Page 890

One class of

T ) has already been defined is the ... ( T ) determined by T provided that we

require the

elements .

One class of

**scalar**functions f , other than polynomials , for which the operator f (T ) has already been defined is the ... ( T ) determined by T provided that we

require the

**scalar**function g ( 2 ) = 1 and the operator T be correspondingelements .

Page 1178

Then K maps

from Plancherel's theorem that K is a bounded mapping of the space L , of

- valued functions into the space L2 ( 12 ) of square - integrable vector - valued ...

Then K maps

**scalar**- valued functions into functions with values in l2 . It is plainfrom Plancherel's theorem that K is a bounded mapping of the space L , of

**scalar**- valued functions into the space L2 ( 12 ) of square - integrable vector - valued ...

Page 1782

Thus the norm in a direct sum of Hilbert spaces is always given by ( iii ) . To

summarize , we state the following definition . 17 DEFINITION . For each i 1 , .. ... ,

n , let H ; be a Hilbert space with

Hilbert ...

Thus the norm in a direct sum of Hilbert spaces is always given by ( iii ) . To

summarize , we state the following definition . 17 DEFINITION . For each i 1 , .. ... ,

n , let H ; be a Hilbert space with

**scalar**products ( • , ) ;. The direct sum of theHilbert ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad 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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero