Linear Operators: Spectral operators |
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Page 1967
... inverse in Y has this inverse also in X. e = = - = - -1 PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so ee * = ( ee * ) * = e ** e * = ee * e * . Now let x in X have the inverse x in . Then ( x - 1 ) * x ...
... inverse in Y has this inverse also in X. e = = - = - -1 PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so ee * = ( ee * ) * = e ** e * = ee * e * . Now let x in X have the inverse x in . 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 . 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 . -1 PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in " 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 ( 5 " ) then , by Corollary 9.6 , A - 1 is in " and the determinant 8 = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero