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

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Page 2081

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. where the supremum is taken over all finite sets { E ; } which

are mutually

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. where the supremum is taken over all finite sets { E ; } which

are mutually

**disjoint**in the sense that E , Ex = 0 , j # k . Show that there exists a ...Page 2190

... On are

If | e = 10101 . If E ( 010 ) . Xo = 20 70 , then S ( f ) xo = Qi , Xo and S ( f ) 2 lail =

lfe . This establishes the final inequality of the theorem . From this inequality it is ...

... On are

**disjoint**sets in E whose union is 1 . There is an io sn with E ( die ) 0 andIf | e = 10101 . If E ( 010 ) . Xo = 20 70 , then S ( f ) xo = Qi , Xo and S ( f ) 2 lail =

lfe . This establishes the final inequality of the theorem . From this inequality it is ...

Page 2266

A projection Ee B will be said to satisfy the countable chain condition if every

family of

denote by 6 the set of all Ee B satisfying this condition . It will be shown that C is a

...

A projection Ee B will be said to satisfy the countable chain condition if every

family of

**disjoint**projections in B bounded by E is at most countable . We shalldenote by 6 the set of all Ee B satisfying this condition . It will be shown that C is a

...

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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