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 ( T ) where П ≤ X ** , then it has a unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( F ) ...
... unique resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( T ) where П ≤ X ** , then it has a unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( F ) ...
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 2265
... unique follows easily from the distributivity . Q.E.D. 3 THEOREM . Let m be a multiplicity function on a complete Boolean algebra B of projections in a B - space X. Then there is a unique family { E } of disjoint elements in B , n ...
... unique follows easily from the distributivity . Q.E.D. 3 THEOREM . Let m be a multiplicity function on a complete Boolean algebra B of projections in a B - space X. Then there is a unique family { E } of disjoint elements in B , n ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero