## Linear Operators, Part 2 |

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Page 898

If E is the resolution of the

of complex numbers, then E(6)T = TE(6), a(T,) where T, is the restriction of T to E(

6).§}. HF) 9"' Paoor". The first statement follows from Theorem l(ii). Now for 5 ¢ 5 ...

If E is the resolution of the

**identity**for the normal operator T and if 6 is a Borel setof complex numbers, then E(6)T = TE(6), a(T,) where T, is the restriction of T to E(

6).§}. HF) 9"' Paoor". The first statement follows from Theorem l(ii). Now for 5 ¢ 5 ...

Page 920

Let E and E be the resolutions of the

Corollary 2.7 it is seen that E = VEV'1 and hence that F(T) = VF(T)V—1 for every

bounded Borel function F. The mapping VV = UV of Si) onto 2:11 L2(€,,, ii) is

clearly an ...

Let E and E be the resolutions of the

**identity**for T and T respectively. FromCorollary 2.7 it is seen that E = VEV'1 and hence that F(T) = VF(T)V—1 for every

bounded Borel function F. The mapping VV = UV of Si) onto 2:11 L2(€,,, ii) is

clearly an ...

Page 1717

By induction on |J,|, we can readily show that a formal

'3"'+ Z CJ'JlllJ(tl')8J, l-/|<|-/;|+l-7|! with suitable coefficients C_,__,l, holds for every

function C in C§°(Io). Making use of

By induction on |J,|, we can readily show that a formal

**identity**5"1C(.v)3"'=C(.2')3J'3"'+ Z CJ'JlllJ(tl')8J, l-/|<|-/;|+l-7|! with suitable coefficients C_,__,l, holds for every

function C in C§°(Io). Making use of

**identities**of the type (1 ), we may evidently ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero