## Linear Operators: Spectral operators |

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Page 889

As will be seen in the next section, a normal operator T in Hilbert space ()

determines a spectral measure which is defined on the Boolean algebra 3 of all

measure ...

As will be seen in the next section, a normal operator T in Hilbert space ()

determines a spectral measure which is defined on the Boolean algebra 3 of all

**Borel sets**in the plane and which satisfies (iv) for every 6 e 3. This spectralmeasure ...

Page 894

*I, f(s) | g(t)}{dt), s, f(s) olds oo). refer to the integral of f with respect to the additive

operator valued set functions whose values on a set a e 2 are | g(t). ... 6.2) that r*

E(0) = 0 for every

*I, f(s) | g(t)}{dt), s, f(s) olds oo). refer to the integral of f with respect to the additive

operator valued set functions whose values on a set a e 2 are | g(t). ... 6.2) that r*

E(0) = 0 for every

**Borel set**6 in S and every pair r, wo with we ?:, r* e to.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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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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