Linear Operators, Part 2 |
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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 ( μI — T — P ) x = C ( I – PR ( μi ; T ) ) ( μiI — T ) x = R ( μi ; 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 . - k - l Since by ...
... C ( μI — T — P ) x = C ( I – PR ( μi ; T ) ) ( μiI — T ) x = R ( μi ; 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 . - k - l Since by ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero