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

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Page 1913

In Chapter XV we try to stress most of the basic elementary

operators that distinguish them from other operators . These

variety of forms not immediately apparent from the definition of a spectral ...

In Chapter XV we try to stress most of the basic elementary

**properties**of spectraloperators that distinguish them from other operators . These

**properties**assume avariety of forms not immediately apparent from the definition of a spectral ...

Page 2134

Statement of the Problem In the preceding chapter we studied the

bounded spectral operators , that is , operators which have a countably additive

resolution of the identity defined on the field of Borel sets . These operators were

...

Statement of the Problem In the preceding chapter we studied the

**properties**ofbounded spectral operators , that is , operators which have a countably additive

resolution of the identity defined on the field of Borel sets . These operators were

...

Page 2588

13 ( 2055 - 2063 ) Direct sum H " , equivalence between M , ( B ( H ) ) and B ( HP

) . XV . 9 ( 19611963 ) operators and their adjoints on , XV . 9 ( 1960 - 1963 )

Discrete operator , definition of , XIX . 2 . 1 ( 2291 )

) ...

13 ( 2055 - 2063 ) Direct sum H " , equivalence between M , ( B ( H ) ) and B ( HP

) . XV . 9 ( 19611963 ) operators and their adjoints on , XV . 9 ( 1960 - 1963 )

Discrete operator , definition of , XIX . 2 . 1 ( 2291 )

**properties**of , XIX . 2 . 2 ( 2292) ...

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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