Linear Operators: Spectral operators |
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Page 2461
... class C ; moreover , V and R have the same norm as elements of свр 11 COROLLARY . An operator V belonging to the trace class C1 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 свр 11 COROLLARY . An operator V belonging to the trace class C1 can be factored as V = AB , where A and B belong to the Hilbert - Schmidt class HS = 62 , and where the ...
Page 2501
... trace class ; ( ii ) the operators E ( RG ) E ( G ) are all compact . Then the strong limits limť → ± ∞ ettH2e - itHi E ( G ) exist . 1 土± ∞ 1 2 As a consequence of this result , it follows that if H1 and H2 are a pair of Hermitian ...
... trace class ; ( ii ) the operators E ( RG ) E ( G ) are all compact . Then the strong limits limť → ± ∞ ettH2e - itHi E ( G ) exist . 1 土± ∞ 1 2 As a consequence of this result , it follows that if H1 and H2 are a pair of Hermitian ...
Page 2502
... trace class of operators . Krein proves that the function log 4 ( z ) has the integral representation + ∞ log 4 ( z ) ... trace norm of Chapter XI . Moreover , Krein establishes the trace formula tr ( pH , ) − p ( H ) = [ 8 ( ) ( ) ĐÃ ...
... trace class of operators . Krein proves that the function log 4 ( z ) has the integral representation + ∞ log 4 ( z ) ... trace norm of Chapter XI . Moreover , Krein establishes the trace formula tr ( pH , ) − p ( H ) = [ 8 ( ) ( ) ĐÃ ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero