Linear Operators, Part 2 |
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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 ( H " ) and M , ( B ( H ) ) , for if 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 ( H " ) and M , ( B ( H ) ) , for if 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 e2nin , 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 e2nin , 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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 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