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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Results 1-3 of 80
Page 2391
... lemma . Q.E.D. - 1 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 << ∞ . Suppose in the notation of Lemma 4 that A + ( λ1 ) ‡ 0 , A ̄ ( λ1 ) # 0 . Then for λ = λ1 lying on any sufficiently short transversal to the ...
... lemma . Q.E.D. - 1 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 << ∞ . Suppose in the notation of Lemma 4 that A + ( λ1 ) ‡ 0 , A ̄ ( λ1 ) # 0 . Then for λ = λ1 lying on any sufficiently short transversal to the ...
Page 2395
... lemma . = -2ιμα , ( t , μ ( λ ) ) Q.E.D. 9 COROLLARY . Let the hypotheses of Lemma 7 be satisfied , and in particular let A * ( λ ) and A− ( λ ) be non - vanishing for 0 ≤λ < ∞o . Let f and g be a pair of functions in C [ 0 ...
... lemma . = -2ιμα , ( t , μ ( λ ) ) Q.E.D. 9 COROLLARY . Let the hypotheses of Lemma 7 be satisfied , and in particular let A * ( λ ) and A− ( λ ) be non - vanishing for 0 ≤λ < ∞o . Let f and g be a pair of functions in C [ 0 ...
Page 2479
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to H1 of the operator H of Lemma 15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace H1 , and put V = V2Q . Plainly , V is symmetric ...
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to H1 of the operator H of Lemma 15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace H1 , and put V = V2Q . Plainly , V is symmetric ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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