Linear Operators: Spectral operators |
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Page 1967
... inverse in Y has this inverse also in X. e = in PROOF . We first show that ee e * . Since e is the unit , e * = ee * , and so = - 1 = ee * : ( ee * ) * = e ** e * = ee * = e * . Now let x in X have the inverse x . Then ( x − 1 ) * x ...
... inverse in Y has this inverse also in X. e = in PROOF . We first show that ee e * . Since e is the unit , e * = ee * , and so = - 1 = ee * : ( ee * ) * = e ** e * = ee * = e * . Now let x in X have the inverse x . Then ( x − 1 ) * x ...
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 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are ...
... 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 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are ...
Page 2069
... inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( $ " ) then , by Corollary 9.6 , A - 1 is in Ão and the determinant 8 = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
... inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( $ " ) then , by Corollary 9.6 , A - 1 is in Ão and the determinant 8 = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero