## Linear Operators, Part 2 |

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Page 888

Nelson Dunford, Jacob T. Schwartz. where 0, 6 are arbitrary

where ¢ 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 0, 6 are arbitrary

**spectral sets**andwhere ¢ 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 6 = a(T;) then,

since the

domain of a

subset of ...

Without relaxing the condition (iii) this is clearly impossible, for if 6 = a(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 of ...

Page 933

79], where the relation of the spectra of A and its minimal normal extension and

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

spectra. The

...

79], where the relation of the spectra of A and its minimal normal extension and

other 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

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