## Linear Operators: Spectral theory |

### From inside the book

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Page 853

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 or DS), and an orthogonal projection Q in S),

such that Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29

Let {T,} be a sequence of bounded

exists ...

Then there exists a Hilbert space or DS), and an orthogonal projection Q in S),

such that Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29

Let {T,} be a sequence of bounded

**operators in Hilbert**space Sy. Then thereexists ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero