Linear Operators: Spectral operators |
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Page 2068
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let I be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
... contains all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let I be an ideal in the subalgebra A。 of A and let A ( J ) be the algebra of ...
Page 2069
... contains all 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 ...
... contains all 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 ...
Page 2159
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in To PROOF . If is not in the ...
... contains a non - trivial sub- interval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then the set of points regular relative to T is dense in To PROOF . If is not in the ...
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