## Linear Operators: Spectral theory |

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Page v

The present volume includes all of the material of our earlier announcement

associated with the classical spectral theorem for self adjoint

space. While there are some isolated discussions of nonselfadjoint operators,

such ...

The present volume includes all of the material of our earlier announcement

associated with the classical spectral theorem for self adjoint

**operators in Hilbert**space. While there are some isolated discussions of nonselfadjoint operators,

such ...

Page 1025

Q.E.D. Having established these preliminary theorems on finite dimensional

spaces, we now return to the study of Hilbert space. It is desired to generalize the

notion of trace to certain

appear ...

Q.E.D. Having established these preliminary theorems on finite dimensional

spaces, we now return to the study of Hilbert space. It is desired to generalize the

notion of trace to certain

**operators in Hilbert**space and at first glance it mayappear ...

Page 1262

Then there exists a Hilbert space ^ 2 and an orthogonal projection Q in such that

Ax = PQx, x e$Q, P denoting the orthogonal projection of §j on 29 Let {Tn} be a

sequence of bounded

space ...

Then there exists a Hilbert space ^ 2 and an orthogonal projection Q in such that

Ax = PQx, x e$Q, P denoting the orthogonal projection of §j on 29 Let {Tn} be a

sequence of bounded

**operators in Hilbert**space Then there exists a Hilbertspace ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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