## Linear Operators: Spectral theory |

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Page 889

1.5), every set in the domain of a spectral measure satisfying (iii) is necessarily

an open and closed subset of a(T) and thus ... <=i <~i A spectral measure E

defined on the

(v) for ...

1.5), every set in the domain of a spectral measure satisfying (iii) is necessarily

an open and closed subset of a(T) and thus ... <=i <~i A spectral measure E

defined on the

**Borel sets**in the plane and satisfying (iv) for every**Borel set**d and(v) for ...

Page 894

6.2) that x*E(6)x = 0 for every

e 36*. It follows (II. 3.15) that E(6) = 0. Thus if E and A are bounded additive

regular operator valued set functions defined on the

topological ...

6.2) that x*E(6)x = 0 for every

**Borel set**8 in S and every pair a;, x* with x e 36, x*e 36*. It follows (II. 3.15) that E(6) = 0. Thus if E and A are bounded additive

regular operator valued set functions defined on the

**Borel sets**of a normaltopological ...

Page 913

Then {an} is a decreasing sequence of

such that if e is a Borel subset of a'n and 2S* vAe) = °> then Vn(') = 0- Put x = ^(at

)Vj • T° see that x is maximal let e be a

Then {an} is a decreasing sequence of

**Borel sets**such that 2"^o vAan) — °> an^such that if e is a Borel subset of a'n and 2S* vAe) = °> then Vn(') = 0- Put x = ^(at

)Vj • T° see that x is maximal let e be a

**Borel set**for which (E(e)x,x) = \E(e)x\* = 0 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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