Linear Operators: Spectral operators |
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Page 2308
... Theorem XIII.2.10 and by Lemma XII.1.6 ( a ) , it follows from Definition XIII.2.17 and the remark preceding Definition XIII.2.29 , that S is closed . From this , it follows immediately that S - XI is closed , and hence from Lemma XII ...
... Theorem XIII.2.10 and by Lemma XII.1.6 ( a ) , it follows from Definition XIII.2.17 and the remark preceding Definition XIII.2.29 , that S is closed . From this , it follows immediately that S - XI is closed , and hence from Lemma XII ...
Page 2364
... Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for n < 1 + 81 . It follows from Lemma VII.6.6 that if η O is any bounded open set whose boundary does not ...
... Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for n < 1 + 81 . It follows from Lemma VII.6.6 that if η O is any bounded open set whose boundary does not ...
Page 2479
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to H1 of the operator H of Lemma 15 ( cf ... follows by Lemma 13 that , if is sufficiently large , we have ( 83 ) 1 ( λ 。 I — H1 ) − 1 — ( λ \。 I — H ) − 1 ( I ...
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to H1 of the operator H of Lemma 15 ( cf ... follows by Lemma 13 that , if is sufficiently large , we have ( 83 ) 1 ( λ 。 I — H1 ) − 1 — ( λ \。 I — H ) − 1 ( I ...
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