Linear Operators: Spectral operators |
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Results 1-3 of 25
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero