## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

### From inside the book

Results 1-3 of 90

Page 2225

isomorphic ( as a Boolean algebra ) to the ... Most of the results in Section 3 are

due to Bade [ 3 , 4 ] although special cases of some of these theorems were

**Prove**that every complete Boolean algebra of projections in a B - space isisomorphic ( as a Boolean algebra ) to the ... Most of the results in Section 3 are

due to Bade [ 3 , 4 ] although special cases of some of these theorems were

**proved**...Page 2459

Statement ( b ) of our lemma follows at once . If xn e Lac ( H ) and limn + Xn = x ,

then , by what we have already

e Lac ( H ) and Y2 , Y3 are orthogonal to Lac ( H ) . But , since xn € Lac ( H ) we ...

Statement ( b ) of our lemma follows at once . If xn e Lac ( H ) and limn + Xn = x ,

then , by what we have already

**proved**, we may write x = y1 + y2 + Ys , where yıe Lac ( H ) and Y2 , Y3 are orthogonal to Lac ( H ) . But , since xn € Lac ( H ) we ...

Page 2462

Therefore T . C . SEM + 1 ) for nano ,

VI . 5 . 2 , C * is a compact operator . Thus , by what we have already

TnC * 0 as n + 00 . But ICT * 1 = | ( T , C * ) * 1 = 1T , C * , so ( CT * | - 0 as n → 00

...

Therefore T . C . SEM + 1 ) for nano ,

**proving**| T , Cl →0 as n + 00 . By TheoremVI . 5 . 2 , C * is a compact operator . Thus , by what we have already

**proved**,TnC * 0 as n + 00 . But ICT * 1 = | ( T , C * ) * 1 = 1T , C * , so ( CT * | - 0 as n → 00

...

### What people are saying - Write a review

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

### Other editions - View all

### Common terms and phrases

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