Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2082
... separable space L ( 01 , μ ) onto a closed separable subspace sp { E ( o ) xo | σe } of X. This contradiction shows that a spectral measure cannot satisfy such a Lipschitz condition . 51 ( McCarthy ) Let 2 , μ be as in the preceding ...
... separable space L ( 01 , μ ) onto a closed separable subspace sp { E ( o ) xo | σe } of X. This contradiction shows that a spectral measure cannot satisfy such a Lipschitz condition . 51 ( McCarthy ) Let 2 , μ be as in the preceding ...
Page 2099
... separable reflexive B - space need not be a spectral operator . In the affirmative direction Foguel [ 2 ] noted that in any space the sum ( or product ) of two commuting spectral operators is spectral if and only if the sum ( or product ) ...
... separable reflexive B - space need not be a spectral operator . In the affirmative direction Foguel [ 2 ] noted that in any space the sum ( or product ) of two commuting spectral operators is spectral if and only if the sum ( or product ) ...
Page 2283
... separable , then m ( E ) = m ( E * ) for every E = B. Eo n PROOF . For each integer n let E , and F * be respectively the projec- tions of uniform multiplicity n of Theorems 8 and 24. Then , in view of Theorem 32 , F * E * , the adjoint ...
... separable , then m ( E ) = m ( E * ) for every E = B. Eo n PROOF . For each integer n let E , and F * be respectively the projec- tions of uniform multiplicity n of Theorems 8 and 24. Then , in view of Theorem 32 , F * E * , the adjoint ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero