## Linear Operators: Spectral operators |

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Page 888

Nelson Dunford, Jacob T. Schwartz. where a, 6 are arbitrary

where q is the void set. Here we have used the notations A A B and A v B for the

intersection and union of two commuting projections A and B. We recall that

these ...

Nelson Dunford, Jacob T. Schwartz. where a, 6 are arbitrary

**spectral**sets andwhere q is the void set. Here we have used the notations A A B and A v B for the

intersection and union of two commuting projections A and B. We recall that

these ...

Page 889

Without relaxing the condition (iii) this is clearly impossible, for if Ó = o(T,) then,

since the

domain of a

subset ...

Without relaxing the condition (iii) this is clearly impossible, for if Ó = o(T,) then,

since the

**spectrum**of an operator is always closed (IX.1.5), every set in thedomain of a

**spectral**measure satisfying (iii) is necessarily an open and closedsubset ...

Page 933

79], where the relation of the

other questions are investigated. Halmos [9] also considers the relation of the

...

79], where the relation of the

**spectra**of A and its minimal normal extension andother questions are investigated. Halmos [9] also considers the relation of the

**spectra**. The**spectral**sets of von Neumann. If T is a bounded linear operator in a...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### 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