Linear Operators: Spectral operators |
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Results 1-3 of 91
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 ) , σ ( x ) ≤ 8 , - SES ( T ) , σ ( x ) ≤ d ' . This spectral measure is ...
... 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 ) , σ ( x ) ≤ 8 , - SES ( T ) , σ ( x ) ≤ d ' . This spectral measure is ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero