## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 73

Page 1012

from which it follows that || T - Tmll Sɛ for m > m ( s ) and completes the

from which it follows that || T - Tmll Sɛ for m > m ( s ) and completes the

**proof**that HS is a B - space under the Hilbert - Schmidt norm . Finally , let T be in HS and let B be any bounded linear operator in H. Then || BT || 2 ...Page 1179

**Proof**. We saw in the course of proving Theorem 25 that the mapping M X which sends a scalar - valued function with the Fourier transform ( 5 ) into the vector - valued function whose nth component has the Fourier transform İn ...Page 1459

**PROOF**. It is obvious from Definition 20 that t is bounded below . Thus the present corollary follows from Corollary 7 and Definition 25 ( b ) . Q.E.D. 31 COROLLARY . Suppose in addition to the hypotheses of Theorem 8 that the ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

44 other sections not shown

### Common terms and phrases

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