## Linear Operators: Spectral theory |

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Results 1-3 of 88

Page 1297

The first

Now Ti(t) is an adjoint (Theorem 10); therefore (cf. XII.1.6) £(T(r)) is complete in

the

of ...

The first

**norm**is the**norm**of the pair [f, Tif) as an element of the graph of Ti(t).Now Ti(t) is an adjoint (Theorem 10); therefore (cf. XII.1.6) £(T(r)) is complete in

the

**norm**||f||1. Since the two additional terms in f2 are the**norm**of f as an elementof ...

Page 1431

Leto, and 3), be the closures of £(To(t')) in the

respectively. By step (c) we have that Q, Doi. Let ge og, and let {gn} be a Cauchy

sequence in Q(To(t')) which converges to g in the

is in ...

Leto, and 3), be the closures of £(To(t')) in the

**norms**of Q(Ti(r')) and £(Ti(t))respectively. By step (c) we have that Q, Doi. Let ge og, and let {gn} be a Cauchy

sequence in Q(To(t')) which converges to g in the

**norm**of £(Ti(t)). To show that gis in ...

Page 1639

Then for a function f in one of the spaces C*(I), C*(I), or C.(I), we place a(f; J, m) =

sup|6"f(r), are Kn and define the

. m) . *To so so. 2"2"j! 1+u(f; J, m) This

Then for a function f in one of the spaces C*(I), C*(I), or C.(I), we place a(f; J, m) =

sup|6"f(r), are Kn and define the

**norm**of f by the equation co k - |f| = X X o * - u(f, J. m) . *To so so. 2"2"j! 1+u(f; J, m) This

**norm**makes each of the spaces listed ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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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