## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 85

Page 888

where a, 6 are arbitrary

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 operators are defined by the

...

where a, 6 are arbitrary

**spectral**sets and where q is the void set. Here we haveused 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 operators are defined by the

...

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...

Page 1920

(See also Ordered representation)

function, XI.4.10 (988) definition, VII.3.17 (572) properties, VII.3.19–21 (574–575)

of von Neumann, X.9 (933)

(See also Ordered representation)

**Spectral**set, of a bounded measurablefunction, XI.4.10 (988) definition, VII.3.17 (572) properties, VII.3.19–21 (574–575)

of von Neumann, X.9 (933)

**Spectral**synthesis, problem of, XI.4 (987)**Spectral**...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero