Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2056
... assumed that man's fate was determined by himself but not by an act of free will . Plato ( 427-347 B.C. ) and Socrates ( 469-399 ? B.C. ) assumed that one's decisions were made for one's own good and thus in any situation a man's ...
... assumed that man's fate was determined by himself but not by an act of free will . Plato ( 427-347 B.C. ) and Socrates ( 469-399 ? B.C. ) assumed that one's decisions were made for one's own good and thus in any situation a man's ...
Page 2150
... assumed , without loss of generality , that do ( T ) . Since o ( T ) is totally discon- nected , the closed set 8 is an intersection a Sa of spectral sets 8. Now clearly M ( S ) = M ( ( da ) = [ ] M ( da ) , α α α and so to see that M ...
... assumed , without loss of generality , that do ( T ) . Since o ( T ) is totally discon- nected , the closed set 8 is an intersection a Sa of spectral sets 8. Now clearly M ( S ) = M ( ( da ) = [ ] M ( da ) , α α α and so to see that M ...
Page 2151
... assumed that there is a function & = $ ( t , 8 ) which is twice continuously differentiable on its domain -1 ≤t , d ≤ 1 of definition and which has the following properties . The equation ( -1 , 8 ) = ( +1 , 8 ) holds for all 8 in the ...
... assumed that there is a function & = $ ( t , 8 ) which is twice continuously differentiable on its domain -1 ≤t , d ≤ 1 of definition and which has the following properties . The equation ( -1 , 8 ) = ( +1 , 8 ) holds for all 8 in the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ 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