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

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Page 1945

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. is in the radical of the closed commutative subalgebra of B (

X ) generated by I , S , and N . Lemma IX . 1 . 12 ( e ) shows that this radical is ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. is in the radical of the closed commutative subalgebra of B (

X ) generated by I , S , and N . Lemma IX . 1 . 12 ( e ) shows that this radical is ...

Page 2169

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. uniform limit of analytic functions , it follows that this map is

also a homomorphism on the algebra of continuous functions . To see that it is a ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. uniform limit of analytic functions , it follows that this map is

also a homomorphism on the algebra of continuous functions . To see that it is a ...

Page 2528

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. 5 . Boolean algebras of projections of finite multiplicity .

Pacific J . Math . 9 , 681693 ( 1959 ) . 6 . Finite dimensional perturbations in

Banach ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. 5 . Boolean algebras of projections of finite multiplicity .

Pacific J . Math . 9 , 681693 ( 1959 ) . 6 . Finite dimensional perturbations in

Banach ...

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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