Linear Operators: Spectral operators |
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Page 2160
... shown that the vector x y is in the closure of the manifold ( IT ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that x * ( x − y ) = 0 for every linear functional x * which vanishes on ( I − T ) X . If x ...
... shown that the vector x y is in the closure of the manifold ( IT ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that x * ( x − y ) = 0 for every linear functional x * which vanishes on ( I − T ) X . If x ...
Page 2226
... shown that in a complete metrizable locally convex space there may not be a single functional corresponding to x ... shown by a counterexample constructed by C. Foias . Berkson [ 5 ] has shown that this hypothesis is satisfied if the ...
... shown that in a complete metrizable locally convex space there may not be a single functional corresponding to x ... shown by a counterexample constructed by C. Foias . Berkson [ 5 ] has shown that this hypothesis is satisfied if the ...
Page 2266
... shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to if and only if it is the ...
... shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to if and only if it is the ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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