Linear Operators: Spectral operators |
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Page 2141
... assume without loss of generality that σ is void . Since E ( om ) = E ( omo ( T ) ) , by the preceding lemma , we may also assume that om ≤ o ( T ) . Suppose that our assertion is false , so that there is a p > 0 and a vector x such ...
... assume without loss of generality that σ is void . Since E ( om ) = E ( omo ( T ) ) , by the preceding lemma , we may also assume that om ≤ o ( T ) . Suppose that our assertion is false , so that there is a p > 0 and a vector x such ...
Page 2212
... assume , in the proof of ( ix ) , that Since A ( x − y ) = Ax - Ay it follows that - - T ( fx − y ) ( x − y ) = T ... assume that the functions f , and f , are not identically equal and one of them , say f ,, differs from both f and f ...
... assume , in the proof of ( ix ) , that Since A ( x − y ) = Ax - Ay it follows that - - T ( fx − y ) ( x − y ) = T ... assume that the functions f , and f , are not identically equal and one of them , say f ,, differs from both f and f ...
Page 2342
... assume that the order of B , is m1 , and that m1 > m2 > · > My , my + 1 > Mv + 2 > may . Moreover , we may clearly assume that the coefficient of f ( mt ) in the unique expression B ( ƒ ) = [ } = } y , ƒ ( 0 ) + Σ ; = ¿ ñ‚ƒ o ( 1 ) is 1 ...
... assume that the order of B , is m1 , and that m1 > m2 > · > My , my + 1 > Mv + 2 > may . Moreover , we may clearly assume that the coefficient of f ( mt ) in the unique expression B ( ƒ ) = [ } = } y , ƒ ( 0 ) + Σ ; = ¿ ñ‚ƒ o ( 1 ) is 1 ...
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