Linear Operators: Spectral operators |
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Page 2130
... coefficients , while spectral theoretic notions are simpler for complex coefficients . To bridge this gap , we employ the following construction . If x is a real B - space which is ordered by ≤ , let X1 = X → X and define : ( x + iẞ ) ...
... coefficients , while spectral theoretic notions are simpler for complex coefficients . To bridge this gap , we employ the following construction . If x is a real B - space which is ordered by ≤ , let X1 = X → X and define : ( x + iẞ ) ...
Page 2174
... coefficients . Similarly , Kantorovitz [ 7 ; p . 545 ] showed that if x is weakly complete and if for some M > 0 and every polynomial p with real coefficients we have etp ( T ) | ≤ M , then T is a scalar type spectral operator with ...
... coefficients . Similarly , Kantorovitz [ 7 ; p . 545 ] showed that if x is weakly complete and if for some M > 0 and every polynomial p with real coefficients we have etp ( T ) | ≤ M , then T is a scalar type spectral operator with ...
Page 2378
... coefficients which are small at infinity in a sufficiently strong sense . The main part of our analytic work will ... coefficient q of ( 1 ) appears in the following lemma . 1 LEMMA . Let the coefficient q in ( 1 ) satisfy the inequality ...
... coefficients which are small at infinity in a sufficiently strong sense . The main part of our analytic work will ... coefficient q of ( 1 ) appears in the following lemma . 1 LEMMA . Let the coefficient q in ( 1 ) satisfy the inequality ...
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