Linear Operators, Part 2 |
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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 : 1 ( a + 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 : 1 ( a + 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 real ...
... 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 real ...
Page 2338
... coefficients a and b are identical up to a common factor of modulus 1 with the coefficients ã , and b , of equation ( 48 ) . Thus , for a normalized set of boundary conditions , Hypotheses 9 and 10 depend only on the " leading " ...
... coefficients a and b are identical up to a common factor of modulus 1 with the coefficients ã , and b , of equation ( 48 ) . Thus , for a normalized set of boundary conditions , Hypotheses 9 and 10 depend only on the " leading " ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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