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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Results 1-3 of 19
Page 1946
... orthogonal to B5 . If y is orthogonal to BH , then 0 = ( B2y , y ) = ( By , By ) and so By = 0. Since B has an inverse , y = 0. This proves that B is a self adjoint linear homeo- morphism of H onto all of 5. Now , since T * AT A we have ...
... orthogonal to B5 . If y is orthogonal to BH , then 0 = ( B2y , y ) = ( By , By ) and so By = 0. Since B has an inverse , y = 0. This proves that B is a self adjoint linear homeo- morphism of H onto all of 5. Now , since T * AT A we have ...
Page 2170
... orthogonal vectors x , y satisfy the relation | x + y | 2 : | x | 2 + | y | 2 , it will suffice to show that x is orthogonal to y if their spectra o ( x ) and o ( y ) , relative to the self adjoint operator T , are disjoint . In this ...
... orthogonal vectors x , y satisfy the relation | x + y | 2 : | x | 2 + | y | 2 , it will suffice to show that x is orthogonal to y if their spectra o ( x ) and o ( y ) , relative to the self adjoint operator T , are disjoint . In this ...
Page 2216
... orthogonal projection onto Ho then , since E ( e ) leaves Ho invariant , PE ( e ) P = E ( e ) P . If y is orthogonal to Ho , ( E ( e ) y , So ) = ( y , E ( e ) Ho ) = 0 , so that E ( e ) y is orthogonal to Ho . Thus E ( e ) leaves the ...
... orthogonal projection onto Ho then , since E ( e ) leaves Ho invariant , PE ( e ) P = E ( e ) P . If y is orthogonal to Ho , ( E ( e ) y , So ) = ( y , E ( e ) Ho ) = 0 , so that E ( e ) y is orthogonal to Ho . Thus E ( e ) leaves the ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
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