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 2130
... B - space which is ordered by ≤ , let 1 = XX and define : ( a + iß ) [ x , y ] = [ ax − ẞy , xy + ẞx ] , α , ẞ = R , x , y = X ; 1 [ [ x , y ] = sup [ x1 , y1 ] [ x2 , y2 ] 1 , 1 ( cos 0 ) x + ( sin 0 ) y | ; 0≤0≤2r whenever X1 x 2 ...
... B - space which is ordered by ≤ , let 1 = XX and define : ( a + iß ) [ x , y ] = [ ax − ẞy , xy + ẞx ] , α , ẞ = R , x , y = X ; 1 [ [ x , y ] = sup [ x1 , y1 ] [ x2 , y2 ] 1 , 1 ( cos 0 ) x + ( sin 0 ) y | ; 0≤0≤2r whenever X1 x 2 ...
Page 2193
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
Page 2484
... B ( 8 , σ ) + ∞ - σ τ ίε do = 9 ] B ( s , σ ) 80 8 - σ do in A ( s , 8 ) . Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued function defined for all s and t ...
... B ( 8 , σ ) + ∞ - σ τ ίε do = 9 ] B ( s , σ ) 80 8 - σ do in A ( s , 8 ) . Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued function defined for all s and t ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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 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