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 2112
... sets , and G1 and G2 are open 1 sets which cover C. ( It should be noted that T and T * play symmetric roles in ( i ) and ( iv ) . ) An example is given to show that not every operator admits a duality theory of type 1 ; however , if T ...
... sets , and G1 and G2 are open 1 sets which cover C. ( It should be noted that T and T * play symmetric roles in ( i ) and ( iv ) . ) An example is given to show that not every operator admits a duality theory of type 1 ; however , if T ...
Page 2203
... open set . Let e be an open subset of 4 , let x and x * be elements of X , X * , respectively , and let ɛ > 0 . Then , because of the regularity of xA ( · ) x * , there is a closed subset 8 of e such that ( i ) 1 E \ xA ( 81 ) x * -xA ...
... open set . Let e be an open subset of 4 , let x and x * be elements of X , X * , respectively , and let ɛ > 0 . Then , because of the regularity of xA ( · ) x * , there is a closed subset 8 of e such that ( i ) 1 E \ xA ( 81 ) x * -xA ...
Page 2233
... open set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( n = 1 en ) = I. The operator f ( T ) is defined by the equations D ( ƒ ( T ) ) = { x | lim ...
... open set U such that E ( U ) I. Let { e } be an arbitrary increasing sequence of bounded Borel sets with closures contained in U , such that E ( n = 1 en ) = I. The operator f ( T ) is defined by the equations D ( ƒ ( T ) ) = { x | lim ...
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