Linear Operators: Spectral operators |
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Page 2084
... C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( λ ; C ) — I λ 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ...
... C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( λ ; C ) — I λ 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ...
Page 2184
... C ) = I is satisfied by the operator CNS - 1T - 1 . Since N is in the radical R , so is C , which shows that T - 1 - S - 1 + C is in the algebra A ( B ) R and proves that this algebra is a full algebra . Q.E.D. = Having established the ...
... C ) = I is satisfied by the operator CNS - 1T - 1 . Since N is in the radical R , so is C , which shows that T - 1 - S - 1 + C is in the algebra A ( B ) R and proves that this algebra is a full algebra . Q.E.D. = Having established the ...
Page 2365
... C ( μITP ) x = C ( I – PR ( μi ; T ) ) ( μil — T ) x - Rui ; T ) ( μi I- T ) x = x , x = D ( T ) = D ( T + P ) . Thus Rui ; T + P ) exists and equals C , proving by Definition 2.1 that TP is discrete . = 0 - k - l - - Since by ...
... C ( μITP ) x = C ( I – PR ( μi ; T ) ) ( μil — T ) x - Rui ; T ) ( μi I- T ) x = x , x = D ( T ) = D ( T + P ) . Thus Rui ; T + P ) exists and equals C , proving by Definition 2.1 that TP is discrete . = 0 - k - l - - Since by ...
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