## Linear Operators: Spectral theory |

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Commutative B - Algebras In case X is a commutative B -

Commutative B - Algebras In case X is a commutative B -

**algebra**every ideal I is two - sided and the quotient**algebra**X / 3 is again a commutative**algebra**.Page 875

The

The

**algebra**B ( H ) of all bounded linear operators in Hilbert space y in which the operation * of involution is defined by equation ( i ) is a B * -**algebra**...Page 979

One of these algebras , namely the

One of these algebras , namely the

**algebra**A of the preceding section , we have met before . For convenience , its definition and some of its properties ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero