Linear Operators: Spectral operators |
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Page 2460
... symmetric operator in H , with domain D ( V ) . Suppose that D ( V ) ≥ D ( H ) , that the operator V ( iI – H ) −1 is compact , and that ( iI — H ) −1V ( iI — H ) −1 is of trace class . Then 1 ( a ) H1 = H + V is a self adjoint ...
... symmetric operator in H , with domain D ( V ) . Suppose that D ( V ) ≥ D ( H ) , that the operator V ( iI – H ) −1 is compact , and that ( iI — H ) −1V ( iI — H ) −1 is of trace class . Then 1 ( a ) H1 = H + V is a self adjoint ...
Page 2466
... symmetric , and that , for λ0 , XI - H has a bounded inverse defined by ( 37 ) ( IH ) -1f = h , where h ( a ) = ( — a ) ̄1ƒ , ( a ) . Thus , by Lemma XII.1.2 , H is closed , and , by XII.4.13 ( b ) , H is self adjoint . We leave it to ...
... symmetric , and that , for λ0 , XI - H has a bounded inverse defined by ( 37 ) ( IH ) -1f = h , where h ( a ) = ( — a ) ̄1ƒ , ( a ) . Thus , by Lemma XII.1.2 , H is closed , and , by XII.4.13 ( b ) , H is self adjoint . We leave it to ...
Page 2478
... symmetric operator in H , that D ( V4 ) ≥ D ( H4 ) , that the operator V4 ( iI – H1 ) ̄1 is compact , and that for each bounded interval e of the real axis the operator ( il — H1 ) ̄1VE4 ( e ) is of trace class . Then - = 1 ( a ) H5 ...
... symmetric operator in H , that D ( V4 ) ≥ D ( H4 ) , that the operator V4 ( iI – H1 ) ̄1 is compact , and that for each bounded interval e of the real axis the operator ( il — H1 ) ̄1VE4 ( e ) is of trace class . Then - = 1 ( a ) H5 ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 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