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 |
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Page 1967
... inverse in has this inverse also in X. = PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e ** e * ee * = e * . Now let x in X have the inverse x - 1 in . Then ( x - 1 ) * x * = ( xx ...
... inverse in has this inverse also in X. = PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e ** e * ee * = e * . Now let x in X have the inverse x - 1 in . Then ( x - 1 ) * x * = ( xx ...
Page 2065
... inverse in A if â ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those ...
... inverse in A if â ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those ...
Page 2069
... inverses . Then Ag contains all inverses . = PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in 2o and the determinant 8 = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
... inverses . Then Ag contains all inverses . = PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in 2o and the determinant 8 = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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