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 90
Page 2391
... lemma . Q.E.D. 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 << ∞ . Suppose in the notation of Lemma 4 that A + ( \ 1 ) # 0 , A ̄ ( 1 ) 0 . Then for λ = λ , lying on any sufficiently short transversal to the real ...
... lemma . Q.E.D. 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 << ∞ . Suppose in the notation of Lemma 4 that A + ( \ 1 ) # 0 , A ̄ ( 1 ) 0 . Then for λ = λ , lying on any sufficiently short transversal to the real ...
Page 2396
... Lemma 1 ( cf. the graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < 0 . 141 → 00 ЦЕР + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e- itu ; ĝu ( t ) = -iμeituƒμ ( t ) + eituƒ “ ( t ) ~ -iμe ...
... Lemma 1 ( cf. the graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < 0 . 141 → 00 ЦЕР + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e- itu ; ĝu ( t ) = -iμeituƒμ ( t ) + eituƒ “ ( t ) ~ -iμe ...
Page 2461
... Lemma XI.9.9 ( e ) ) . The operator V may also be factored as V = CD , where C is compact , and where D is of trace class . PROOF OF LEMMA 10. We note from Theorem XII.7.7 that in the canonical factorization V = QR the initial domain of ...
... Lemma XI.9.9 ( e ) ) . The operator V may also be factored as V = CD , where C is compact , and where D is of trace class . PROOF OF LEMMA 10. We note from Theorem XII.7.7 that in the canonical factorization V = QR the initial domain of ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero