## Linear Operators: Spectral operators |

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Page 1909

Preface As stated in the Preface to Part I of this treatise , our original intention

was to include the

think ) that this

much ...

Preface As stated in the Preface to Part I of this treatise , our original intention

was to include the

**theory**of spectral operators in Part II . We thought ( and stillthink ) that this

**theory**forms an excellent introduction to the detailed study of themuch ...

Page 2112

which cover C . ( iii ) The operator T admits a duality

open sets G2 , . . . , Gn which cover the complex plane , there exist closed linear

subspaces Mi , . . . , Mn which span X , are invariant under T , and such that o ( T

...

which cover C . ( iii ) The operator T admits a duality

**theory**of type 3 if for arbitraryopen sets G2 , . . . , Gn which cover the complex plane , there exist closed linear

subspaces Mi , . . . , Mn which span X , are invariant under T , and such that o ( T

...

Page 2510

monograph by Colojoară and Foiaş [ 4 ] . A variety of more or less related results

on the existence of invariant subspaces for an operator T are given by Wermer [ 1

...

**theory**of spectral operators . These matters are systematically discussed in themonograph by Colojoară and Foiaş [ 4 ] . A variety of more or less related results

on the existence of invariant subspaces for an operator T are given by Wermer [ 1

...

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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