Linear Operators: Spectral operators |
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Page 2218
... sequence in B and suppose that its limit E is a projection . It must be shown that { E } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E - E } shows that it may be assumed that E = 0 . Thus ...
... sequence in B and suppose that its limit E is a projection . It must be shown that { E } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E - E } shows that it may be assumed that E = 0 . Thus ...
Page 2310
... sequence of functions all defined in R1 . Let { g } be a sequence of functions defined in R1 , and suppose that , for each N , ― N Ž lim m3 fm ( w ) — Σ In ( w ) m m1∞ n = 0 == = 0 uniformly for w in R1 . Then we say that the sequence ...
... sequence of functions all defined in R1 . Let { g } be a sequence of functions defined in R1 , and suppose that , for each N , ― N Ž lim m3 fm ( w ) — Σ In ( w ) m m1∞ n = 0 == = 0 uniformly for w in R1 . Then we say that the sequence ...
Page 2450
... sequence { r } , like the sequence λn , is bounded . Let R be the closed , densely defined , unbounded operator in X whose domain D ( R ) consists of all the elements x == 1 ax in x for which Σ = r2 | α , 12 Σε is finite , and which is ...
... sequence { r } , like the sequence λn , is bounded . Let R be the closed , densely defined , unbounded operator in X whose domain D ( R ) consists of all the elements x == 1 ax in x for which Σ = r2 | α , 12 Σε is finite , and which is ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero