Linear Operators, Part 2 |
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Page 2318
... dimensional space or is zero . But , by ( iv ) , I lim ( 1 - B ( A ) ) - ( 1 - E ) - m → ∞ Hence , by Lemma VII.6.7 , = m 00 Ι - Σ Ε ( λ . ) n = m = -0 . n = m has a finite dimensional range for all sufficiently large m , and hence ...
... dimensional space or is zero . But , by ( iv ) , I lim ( 1 - B ( A ) ) - ( 1 - E ) - m → ∞ Hence , by Lemma VII.6.7 , = m 00 Ι - Σ Ε ( λ . ) n = m = -0 . n = m has a finite dimensional range for all sufficiently large m , and hence ...
Page 2403
... dimensional Lebesgue measure . A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but consider- ably generalized result ( Theorem 7 ) whose hypotheses accord , in a general ...
... dimensional Lebesgue measure . A first application ( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but consider- ably generalized result ( Theorem 7 ) whose hypotheses accord , in a general ...
Page 2487
... dimensional complement , such that W ( H + T ) f = HWƒ for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that ac ( H + T ) has a finite dimensional complement , so ...
... dimensional complement , such that W ( H + T ) f = HWƒ for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that ac ( H + T ) has a finite dimensional complement , so ...
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