Linear Operators: Spectral operators |
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Page 1945
... weak product topology so that , by definition , the sets { ƒ | ƒ = L , \ f ( x , y ) − g ( x , y ) ) < ε } , where x , y H and ɛ > 0 , form a subbase for the neighborhoods of a point g in 2. It is easily seen that P is a closed set in ...
... weak product topology so that , by definition , the sets { ƒ | ƒ = L , \ f ( x , y ) − g ( x , y ) ) < ε } , where x , y H and ɛ > 0 , form a subbase for the neighborhoods of a point g in 2. It is easily seen that P is a closed set in ...
Page 2160
... weak topology , we have lim ( λn — λ 。) R ( λn ; T ) x = y . n Then ( IT ) y is the weak limit of ― ( ^ n — λo ) ( λ 。 I — T ) R ( λn ; T ) x = ( λn — λo ) x — ( λo — An ) 2 R ( λn ; T ) x , and this limit is clearly zero . Thus ( AIT ) ...
... weak topology , we have lim ( λn — λ 。) R ( λn ; T ) x = y . n Then ( IT ) y is the weak limit of ― ( ^ n — λo ) ( λ 。 I — T ) R ( λn ; T ) x = ( λn — λo ) x — ( λo — An ) 2 R ( λn ; T ) x , and this limit is clearly zero . Thus ( AIT ) ...
Page 2490
... weak topology ; 1 ( b ) if W + ( H2 , H1 ) w exists , so does W + ( H2 + V1 , H1 ) w and 2 lim W ( H2 + V , H1 ) w = W + ( H2 , H1 ) w || V || 1 → 0 in the strong topology . + 2 6. Notes and Remarks The method used in Section 1 for the ...
... weak topology ; 1 ( b ) if W + ( H2 , H1 ) w exists , so does W + ( H2 + V1 , H1 ) w and 2 lim W ( H2 + V , H1 ) w = W + ( H2 , H1 ) w || V || 1 → 0 in the strong topology . + 2 6. Notes and Remarks The method used in Section 1 for the ...
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