Linear Operators: Spectral operators |
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Page 2239
... follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover , statement ( g ) follows from Corollary 7 . Statement ( d ) is obvious . Letting e e Zo and x = E ( e ) X , we have T ( fxe ) x = lim T ( fxe ) E ( en ) ...
... follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover , statement ( g ) follows from Corollary 7 . Statement ( d ) is obvious . Letting e e Zo and x = E ( e ) X , we have T ( fxe ) x = lim T ( fxe ) E ( en ) ...
Page 2246
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin ... follows that ( sin C ) " P ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin ... follows that ( sin C ) " P ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
Page 2308
... 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.1.5 , that ( S – XI ) -1 is closed . Since this ...
... 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.1.5 , that ( S – XI ) -1 is closed . Since this ...
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