Linear Operators, Part 2 |
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Page 2053
... fact that , in these examples , we have T ( t ) Ho ≤ D ( A® ) if t > 0 ( Hille and Phillips [ 1 , Theorem 10.3.5 , p . 310 ] ) . In the examples of Theorems 19 and 21 we did not appeal to the general theory , as it was clear from the ...
... fact that , in these examples , we have T ( t ) Ho ≤ D ( A® ) if t > 0 ( Hille and Phillips [ 1 , Theorem 10.3.5 , p . 310 ] ) . In the examples of Theorems 19 and 21 we did not appeal to the general theory , as it was clear from the ...
Page 2056
... facts which allows the man to recover only if he calls a physician . These two facts , that of recovering and that of ... fact that man is an incontinent being . Thus man's decisions , which affect his actions and thus determine his ...
... facts which allows the man to recover only if he calls a physician . These two facts , that of recovering and that of ... fact that man is an incontinent being . Thus man's decisions , which affect his actions and thus determine his ...
Page 2225
... fact that if B is a bounded Boolean algebra of projections in a reflexive space then the fact that the strong closure of B is complete follows from a theorem of Day [ 10 ] and was stated explicitly by Dunford [ 2 ] ( see also Bade [ 3 ...
... fact that if B is a bounded Boolean algebra of projections in a reflexive space then the fact that the strong closure of B is complete follows from a theorem of Day [ 10 ] and was stated explicitly by Dunford [ 2 ] ( see also Bade [ 3 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
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