Linear Operators: Spectral operators |
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Page 2200
... projection F in S ( 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 S ( 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 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 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 Fe 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 Fe B there exists a projection ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero