Linear Operators: Spectral operators |
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Page 2094
... unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique resolution of the identity of class ( T ) . Moreover , ( Berkson and Dowson [ 1 ] ) , if T is spectral ...
... unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique resolution of the identity of class ( T ) . Moreover , ( Berkson and Dowson [ 1 ] ) , if T is spectral ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero