Linear Operators, Part 2 |
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Page 2299
... sufficiently large and for μ in Cn , we have - | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 -m ∞ 1 m ≤ 2M dr1 Σ ( λn | + dn ) TM v dñ TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d2 ( λn ] ...
... sufficiently large and for μ in Cn , we have - | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 -m ∞ 1 m ≤ 2M dr1 Σ ( λn | + dn ) TM v dñ TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d2 ( λn ] ...
Page 2349
... sufficiently large m . Since c1 # ĉ1 , we have either c1 > č1 or c1c1 . Suppose for the sake of definiteness that c1 > č1 . Then it is clear that μmμm for sufficiently large m . On the other hand , since -1 -1 —μm - 1 = 2π ( č1 — с1 ) ...
... sufficiently large m . Since c1 # ĉ1 , we have either c1 > č1 or c1c1 . Suppose for the sake of definiteness that c1 > č1 . Then it is clear that μmμm for sufficiently large m . On the other hand , since -1 -1 —μm - 1 = 2π ( č1 — с1 ) ...
Page 2360
... sufficiently large . From this it will then follow as above that the function f ( μ ) Ru ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | TR ( μ ; T ) A | ≤ , for i ...
... sufficiently large . From this it will then follow as above that the function f ( μ ) Ru ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | TR ( μ ; T ) A | ≤ , for i ...
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