## Linear Operators: Spectral theory |

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Page 1126

of the closed set C ; we shall

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 projections

Ei , it ...

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 projections

Ei , it ...

Page 1635

Notational Conventions and Preliminaries Throughout the rest of the present

chapter , the symbol J will

integers . We write JI = k , min J = min , siskli , max J = maxisiskli . It will be

convenient ...

Notational Conventions and Preliminaries Throughout the rest of the present

chapter , the symbol J will

**denote**an index , i . e . , a k - tuple J = [ j1 , . . . , İk ] ofintegers . We write JI = k , min J = min , siskli , max J = maxisiskli . It will be

convenient ...

Page 1636

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

indices for E " , that is , indices whose range of variation is restricted by the

condition min J 21 , max J Sn . The symbols J , , J , will similarly

for En + 1 .

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

**denote**indices for E " , that is , indices whose range of variation is restricted by the

condition min J 21 , max J Sn . The symbols J , , J , will similarly

**denote**indicesfor En + 1 .

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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### Common terms and phrases

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 consider 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 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