## Linear Operators: Spectral theory |

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Page 878

of Bo (a) onto C(g(x)) has the property that a

= u, u e o (a). Clearly the requirement that a and g(u) = u be

elements determines the *-isomorphism uniquely and we are thus led to the

following ...

of Bo (a) onto C(g(x)) has the property that a

**corresponds**to the function a (a '(u))= u, u e o (a). Clearly the requirement that a and g(u) = u be

**corresponding**elements determines the *-isomorphism uniquely and we are thus led to the

following ...

Page 942

By replacing s by st and u by ut and using the fact that u(Et) = u(E) it is seen that s

, g(su-)p(u)n(du) = Ap(st), i.e., every translate p' of an eigenfunction p

eigenfunction ...

By replacing s by st and u by ut and using the fact that u(Et) = u(E) it is seen that s

, g(su-)p(u)n(du) = Ap(st), i.e., every translate p' of an eigenfunction p

**corresponding**to Z is also an eigenfunction**corresponding**to Å. Thus everyeigenfunction ...

Page 1780

An equivalence class U of vectors u, will be said to

class V of vectors v, if there is a pair of vectors, one from U and one from V, with a

non-zero inner product. Suppose that U and V are

An equivalence class U of vectors u, will be said to

**correspond**to an equivalenceclass V of vectors v, if there is a pair of vectors, one from U and one from V, with a

non-zero inner product. Suppose that U and V are

**corresponding**equivalence ...### What people are saying - Write a review

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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