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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Page 2066
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since f * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since f * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
Page 2443
... continuous partial derivatives of all orders up to the second everywhere in the interior of D , and that these derivatives may be extended continuously to the whole of D ; ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and S. g ( x , x ) dx ...
... continuous partial derivatives of all orders up to the second everywhere in the interior of D , and that these derivatives may be extended continuously to the whole of D ; ( ii ) g ( x , x ) > 0 for 0 ≤ x ≤ 1 , and S. g ( x , x ) dx ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero