## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 83

Page 884

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the

Lemma 3.5 by using a fairly deep

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the

**results**given in Section 1 are due. B- and ... In their proof, they provedLemma 3.5 by using a fairly deep

**result**of Šilov that was not generally available.Page 1419

We will show that |f(m,) = f(m;11) = f(m, 12) → ..., which will clearly establish the

desired

= +f(2s, 1–t). We have (-f)" = q.(–f), f = qif, where q1(t) = q(2s, 1.1—t) > q(t), since ...

We will show that |f(m,) = f(m;11) = f(m, 12) → ..., which will clearly establish the

desired

**result**. On the interval [s, 11, m, 1], consider the two functions —f(t) and f(t)= +f(2s, 1–t). We have (-f)" = q.(–f), f = qif, where q1(t) = q(2s, 1.1—t) > q(t), since ...

Page 1591

A

skii and Milman [1]. Theorem 11 was obtained by Weyl for operators of the

second order, and extended by Glazman [1]. The trick used in Theorem 14 has

been ...

A

**result**similar to Lemma 8 can be found in the joint paper of Krein, Krasnosel'skii and Milman [1]. Theorem 11 was obtained by Weyl for operators of the

second order, and extended by Glazman [1]. The trick used in Theorem 14 has

been ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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