Linear Operators: Spectral operators |
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Page 1962
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a ,, ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( S ) and M , ( B ( H ) ) , for if A↔ ( a ...
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a ,, ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( S ) and M , ( B ( H ) ) , for if A↔ ( a ...
Page 2305
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2ninz , n = 0 , 1 ...
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2ninz , n = 0 , 1 ...
Page 2507
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " of the ...
... corresponding to a two- body force in a three - body system ) , then the spectrum of H + V consists of the purely continuous spectrum corresponding to the spectrum of H , a point spectrum corresponding to the " bound states " 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