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 13
Page 2462
... trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . .... PROOF . The set K = C ( { x = H || x | ≤ 1 } ) is conditionally compact , and thus for each ɛ > 0 there exists a finite set x1 ...
... trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . .... PROOF . The set K = C ( { x = H || x | ≤ 1 } ) is conditionally compact , and thus for each ɛ > 0 there exists a finite set x1 ...
Page 2500
... trace class for each x . 1 Results concerning the scattering operator of the sort described above are proved rigorously on the basis of rather general hypotheses in Birman and Krein [ 1 ] . 1 1 In that paper , the scattering operator S ...
... trace class for each x . 1 Results concerning the scattering operator of the sort described above are proved rigorously on the basis of rather general hypotheses in Birman and Krein [ 1 ] . 1 1 In that paper , the scattering operator S ...
Page 2501
... trace class ; ( ii ) the operators E ( RG ) E ( G ) are all compact . Then the strong limits lim → + ∞ eitH2e - itH1 E ( G ) exist . - 1 土- k → ± ∞ 2 1 As a consequence of this result , it follows that if H1 and H2 are a pair of ...
... trace class ; ( ii ) the operators E ( RG ) E ( G ) are all compact . Then the strong limits lim → + ∞ eitH2e - itH1 E ( G ) exist . - 1 土- k → ± ∞ 2 1 As a consequence of this result , it follows that if H1 and H2 are a pair of ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 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