Linear Operators, Part 2 |
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Results 1-3 of 62
Page 2103
... obtained by replacing 1 / λ by any function ƒ ( A ) analytic for λ in a neighborhood of the spectrum of the element a in A1 are extensions of the results to be found in IX.4.10 and IX.4.11 . The elementary Lemma 6 which permits these ...
... obtained by replacing 1 / λ by any function ƒ ( A ) analytic for λ in a neighborhood of the spectrum of the element a in A1 are extensions of the results to be found in IX.4.10 and IX.4.11 . The elementary Lemma 6 which permits these ...
Page 2176
... obtained . Similar results were also obtained by Dollinger [ 1 ] and Sine [ 1 ] under the hypothesis that T satisfies certain types of operational calculi , although their assumptions were quite different in nature . Stampfli [ 12 ] has ...
... obtained . Similar results were also obtained by Dollinger [ 1 ] and Sine [ 1 ] under the hypothesis that T satisfies certain types of operational calculi , although their assumptions were quite different in nature . Stampfli [ 12 ] has ...
Page 2405
... obtained in the extreme case r = ∞ ; we leave it to the reader to give the necessary details . Next let 1≤r≤2 . Let h , be a second non - negative , μ - measurable function defined on S. Then we conclude as above that the integral ...
... obtained in the extreme case r = ∞ ; we leave it to the reader to give the necessary details . Next let 1≤r≤2 . Let h , be a second non - negative , μ - measurable function defined on S. Then we conclude as above that the integral ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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