Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 87
Page 2084
... B ) is analytic for λ 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( \ ; C ) —— I λ • 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
... B ) is analytic for λ 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( λ ; B ) + R ( \ ; C ) —— I λ • 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
Page 2193
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
Page 2484
... B ( s , σ ) - ∞ 8 στίε + ∞0 B ( s , σ ) do = P · do FiπA ( s , 8 ) . 81 s σ Let S be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( H ) -valued function defined for all s and ...
... B ( s , σ ) - ∞ 8 στίε + ∞0 B ( s , σ ) do = P · do FiπA ( s , 8 ) . 81 s σ Let S be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( H ) -valued function defined for all s and ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero