## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

### From inside the book

Results 1-3 of 43

Page 1994

When it exists , a is in A and ( 31 ) a = S ( s ) e ( ds ) , 121 = ess sup | ã ( s ) ] . ess

Stated otherwise , a = F - 18F where F is the Fourier transform in H and A is the

operation of multiplication by the function à . PROOF . Let any

o ...

When it exists , a is in A and ( 31 ) a = S ( s ) e ( ds ) , 121 = ess sup | ã ( s ) ] . ess

Stated otherwise , a = F - 18F where F is the Fourier transform in H and A is the

operation of multiplication by the function à . PROOF . Let any

**converge**for eacho ...

Page 2218

If a generalized sequence of projections in a o - complete Boolean algebra of

projections in a B - space

strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case ...

If a generalized sequence of projections in a o - complete Boolean algebra of

projections in a B - space

**converges**weakly to a projection , then it**converges**strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case ...

Page 2462

Moreover , if C belongs to the trace class C1 , then TnC

trace norm , and CT *

XE H | | 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there exists a

finite ...

Moreover , if C belongs to the trace class C1 , then TnC

**converges**to zero intrace norm , and CT *

**converges**to zero in trace norm . PROOF . The set K = C ( {XE H | | 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there exists a

finite ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero