## Linear Operators: Spectral operators |

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Page 1945

Bounded Spectral Operators in

the bounded spectral operators in a

operators in H ? The central result in this direction is a theorem of Wermer which

...

Bounded Spectral Operators in

**Hilbert Space**What is the relationship betweenthe bounded spectral operators in a

**Hilbert space**H and the bounded normaloperators in H ? The central result in this direction is a theorem of Wermer which

...

Page 2169

Self Adjoint Operators in

how the theory of spectral operators may be applied to yield the classical spectral

theorem in

Self Adjoint Operators in

**Hilbert Space**It is the purpose of this section to showhow the theory of spectral operators may be applied to yield the classical spectral

theorem in

**Hilbert space**, that is , the theorem asserting that a bounded self ...Page 2528

Finite dimensional perturbations in Banach spaces . Amer . ... Weak limits of

powers of a contraction in

spectrale et la théorie spectrale des opérateurs généraux d ' un espace de

Hilbert . Bull .

Finite dimensional perturbations in Banach spaces . Amer . ... Weak limits of

powers of a contraction in

**Hilbert space**. Proc . ... La mesure harmonique -spectrale et la théorie spectrale des opérateurs généraux d ' un espace de

Hilbert . Bull .

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algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete 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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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 strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero