## Linear Operators: Spectral theory |

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Hilbert space H and let E

Hilbert space H and let E

**denote**its resolution of the identity . Then there erists a sequence { x } CH such that H = ( x ; ) , where H ( x ; ) = sp { / ( T ) xilfe Clo ( T ) ) } , and a decreasing sequence { en } of Borel sets such ...Page 1126

of the closed set C ; we shall

of the closed set C ; we shall

**denote**this subspace of L , [ 0 , 1 ] by the symbol L , ( C ) . Since each projection in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of the ...Page 1636

In general , unless the contrary is explicitly stated , J , I , J , etc. , will

In general , unless the contrary is explicitly stated , J , I , J , etc. , will

**denote**indices for E ” , that is , indices whose range of variation is restricted by the condition min J 21 , max J S n .### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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 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