Linear Operators: Spectral operators |
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Page 2391
... lemma . Q.E.D. 1 + 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < λ1 < ∞ . Suppose in the notation of Lemma 4 that A * ( \ 1 ) # 0 , A ̄ ( λ1 ) ‡ 0 . Then for λ = λ1 lying on any sufficiently short transversal to ...
... lemma . Q.E.D. 1 + 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < λ1 < ∞ . Suppose in the notation of Lemma 4 that A * ( \ 1 ) # 0 , A ̄ ( λ1 ) ‡ 0 . Then for λ = λ1 lying on any sufficiently short transversal to ...
Page 2396
... Lemma 1 ( cf. the para- graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < ∞o . 141 → 00 LEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e - itu ; ĝu ( t ) = — iμe stuf „ ( t ) + eituf ...
... Lemma 1 ( cf. the para- graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < ∞o . 141 → 00 LEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e - itu ; ĝu ( t ) = — iμe stuf „ ( t ) + eituf ...
Page 2479
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to 5 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 5 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero