Linear Operators: Spectral operators |
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Page 2094
... unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where I ≤ X ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( Ã ) ...
... unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where I ≤ X ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( Ã ) ...
Page 2143
... unique extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF ...
... unique extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF ...
Page 2184
... unique spectral measure A in X * defined on the Borel sets in A such that xA ( · ) x * is regular and countably additive for x in Xx and x * in X * , and for which S * ( ƒ ) = √ƒ ( \ ) 4 ( d \ ) , ƒ = C ( 4 ) . PROOF . For each x in X ...
... unique spectral measure A in X * defined on the Borel sets in A such that xA ( · ) x * is regular and countably additive for x in Xx and x * in X * , and for which S * ( ƒ ) = √ƒ ( \ ) 4 ( d \ ) , ƒ = C ( 4 ) . PROOF . For each x in X ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero