Linear Operators: Spectral operators |
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Results 1-3 of 40
Page 2300
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is ...
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is ...
Page 2318
... finite dimensional range for all sufficiently large m , and hence , a fortiori , E has a finite dimensional range . Q.E.D. ∞0 11 THEOREM . Let T be the unbounded operator in Hilbert space defined by the formal differential operator ...
... finite dimensional range for all sufficiently large m , and hence , a fortiori , E has a finite dimensional range . Q.E.D. ∞0 11 THEOREM . Let T be the unbounded operator in Hilbert space defined by the formal differential operator ...
Page 2487
... finite dimensional complement , such that W ( H + T ) f = HWƒ for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that ac ( H + T ) has a finite dimensional complement ...
... finite dimensional complement , such that W ( H + T ) f = HWƒ for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that ac ( H + T ) has a finite dimensional complement ...
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