## Linear Operators: Spectral operators |

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Page 889

a e S). i- iA spectral measure E defined on the

satisfying (iv) for every

a e S). i- iA spectral measure E defined on the

**Borel sets**in the plane andsatisfying (iv) for every

**Borel set**6 and (v) for every sequence {6,} of disjoint**Borel****sets**is called a resolution of the identity for T. With this terminology the spectral ...Page 894

6.2) that r* E(0) = 0 for every

to. It follows (II.3.15) that E(0) = 0. Thus if E and A are bounded additive regular

operator valued set functions defined on the

6.2) that r* E(0) = 0 for every

**Borel set**6 in S and every pair r, wo with we ?:, r* eto. It follows (II.3.15) that E(0) = 0. Thus if E and A are bounded additive regular

operator valued set functions defined on the

**Borel sets**of a normal topological ...Page 1218

Let u be a finite positive regular measure on the

R. Then, for every B-space valued u-measurable function f on R and every e > 0

there is a

Let u be a finite positive regular measure on the

**Borel sets**of a topological spaceR. Then, for every B-space valued u-measurable function f on R and every e > 0

there is a

**Borel set**or in R with p(0) < e and such that the restriction of f to the ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero