Linear Operators: Spectral operators |
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Results 1-3 of 22
Page 2012
... evident from the following lemma . 1 LEMMA . Let A , be the operator ( 4 ) and let { om } be a sequence satisfy- ing ( 3 ) . Then ( i ) ( ii ) D ( A ) = { p | lim Aoom & exists } , m18 Аоф A , y = lim Acom P , YED ( A ) . PROOF . Let F ...
... evident from the following lemma . 1 LEMMA . Let A , be the operator ( 4 ) and let { om } be a sequence satisfy- ing ( 3 ) . Then ( i ) ( ii ) D ( A ) = { p | lim Aoom & exists } , m18 Аоф A , y = lim Acom P , YED ( A ) . PROOF . Let F ...
Page 2257
... evident that , assuming T to be a spectral operator and making use of Corollary 23 , we can use all the steps of this argument in reverse and conclude that , conversely , ( a ) must be satisfied . To continue with the main line of our ...
... evident that , assuming T to be a spectral operator and making use of Corollary 23 , we can use all the steps of this argument in reverse and conclude that , conversely , ( a ) must be satisfied . To continue with the main line of our ...
Page 2394
... evident . The conclusions of ( iv ) relative to B ̄ ( f , g , λ ) may be established in the same way . Q.E.D. To 8 LEMMA . Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution o ( t , μ ) of the equation Tσ ...
... evident . The conclusions of ( iv ) relative to B ̄ ( f , g , λ ) may be established in the same way . Q.E.D. To 8 LEMMA . Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution o ( t , μ ) of the equation Tσ ...
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