Linear Operators, Part 2 |
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Page 1958
... separable , then the point and residual spectra of a spectral operator are countable . PROOF . Let T be a spectral operator with scalar part S and resolution of the identity E. It follows from Theorem 6 that op ( T ) U o , ( T ) = { a ...
... separable , then the point and residual spectra of a spectral operator are countable . PROOF . Let T be a spectral operator with scalar part S and resolution of the identity E. It follows from Theorem 6 that op ( T ) U o , ( T ) = { a ...
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 Є B. 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 Є B. 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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