Linear Operators: Spectral operators |
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Page 2265
... disjoint elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \ / \ / En · ( ii ) If En ‡ 0 , E , has uniform multiplicity n . Ꮐ PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform ...
... disjoint elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \ / \ / En · ( ii ) If En ‡ 0 , E , has uniform multiplicity n . Ꮐ PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform ...
Page 2266
... disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying this condition . It will be shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 ...
... disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying this condition . It will be shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 ...
Page 2267
... disjoint projections E , each of which is the carrier of a vector x with | x | ≤ 1. Define x 。== 12- " x . Clearly ... disjoint elements in such that each G is bounded by some Eak and EoV - 1 G. For we may consider families of disjoint ...
... disjoint projections E , each of which is the carrier of a vector x with | x | ≤ 1. Define x 。== 12- " x . Clearly ... disjoint elements in such that each G is bounded by some Eak and EoV - 1 G. For we may consider families of disjoint ...
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