Linear Operators, Part 2 |
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Page 2461
... class C ; moreover , V and R have the same norm as elements of Cp . - 1 11 COROLLARY . An operator V belonging to the trace class 1 can be factored as V AB , where A and B belong to the Hilbert - Schmidt class HS = 62 , and where the ...
... class C ; moreover , V and R have the same norm as elements of Cp . - 1 11 COROLLARY . An operator V belonging to the trace class 1 can be factored as V AB , where A and B belong to the Hilbert - Schmidt class HS = 62 , and where the ...
Page 2462
... trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . n - .... 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 . n - .... 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 1 In that paper , the scattering operator ...
... 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 1 In that paper , the scattering operator ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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