Linear Operators: Spectral operators |
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Page 1951
... bounded linear operator in the space E ( X ) . Let V , be the bounded linear operator in X defined by the equation σ 1 V.x = T1E ( 0 ) x , x = X. Then TV ̧ = E ( ơ ) = V ̧ T , which proves that E ( o ) is in J. It follows from Lemma 1 ...
... bounded linear operator in the space E ( X ) . Let V , be the bounded linear operator in X defined by the equation σ 1 V.x = T1E ( 0 ) x , x = X. Then TV ̧ = E ( ơ ) = V ̧ T , which proves that E ( o ) is in J. It follows from Lemma 1 ...
Page 2143
... bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field ( T ) with the properties E ( 8 ) x = x , = 0 , SES ( T ) , o ( x ) = 8 , = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral ...
... bounded linear operator in the complex B - space X. Then there is a unique spectral measure on the field ( T ) with the properties E ( 8 ) x = x , = 0 , SES ( T ) , o ( x ) = 8 , = 0 , d = S ( T ) , σ ( x ) ≤ d ' . This spectral ...
Page 2162
... bounded linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the ...
... bounded linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 Borel function 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 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