Linear Operators, Part 2 |
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Page 2200
... projection F in ( B ) is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where y is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E , 2 in B such that E , zy = y = Fy ...
... projection F in ( B ) is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where y is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E , 2 in B such that E , zy = y = Fy ...
Page 2266
... projection { E | Ex = x } will be called the carrier projection of x . ( Note that if G is the carrier projection of x and 0 F≤ G , then Fx 0. ) The cyclic subspace M ( x ) spanned by a vector x is sp { Ex | E = B } . A projection E ...
... projection { E | Ex = x } will be called the carrier projection of x . ( Note that if G is the carrier projection of x and 0 F≤ G , then Fx 0. ) The cyclic subspace M ( x ) spanned by a vector x is sp { Ex | E = B } . A projection E ...
Page 2271
... projection of x 。 is the identity I. Thus if 0 ‡ E € B , we have Ex 。 0 , and I satisfies the countable chain condition . It will be con- venient to isolate a portion of the argument . 13 PROPOSITION . If 0 FЄ B there exists a projection ...
... projection of x 。 is the identity I. Thus if 0 ‡ E € B , we have Ex 。 0 , and I satisfies the countable chain condition . It will be con- venient to isolate a portion of the argument . 13 PROPOSITION . If 0 FЄ B there exists a projection ...
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