## Linear Operators: Spectral theory |

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Page 860

A B -

in a B -

= x * + y * , ( xy ) * = y * * * ( x ) * = āx * , ( w * ) * = x . All of the examples ...

A B -

**algebra**X is commutative in case xy = yæ for all x and y in X . An involutionin a B -

**algebra**X is a mapping x → * * of X into itself with the properties ( x + y ) *= x * + y * , ( xy ) * = y * * * ( x ) * = āx * , ( w * ) * = x . All of the examples ...

Page 868

It will be a B -

& which contains I properly determines an ideal F in X / F defined as the set of all

ğ = x + ; with x in I . Conversely every ideal in X / 8 is of this form . 1 THEOREM .

It will be a B -

**algebra**if I is closed ( 1 . 13 ) . It is readily seen that every ideal I in& which contains I properly determines an ideal F in X / F defined as the set of all

ğ = x + ; with x in I . Conversely every ideal in X / 8 is of this form . 1 THEOREM .

Page 979

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. be based

upon two closely related commutative algebras of operators in the Hilbert space

Ly ( R ) . One of these algebras , namely the

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. be based

upon two closely related commutative algebras of operators in the Hilbert space

Ly ( R ) . One of these algebras , namely the

**algebra**A of the preceding section ...### What people are saying - Write a review

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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