Linear Operators: Spectral operators |
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Page 2017
... inequality ( i ) of Theorem 6 holds . Here the set S1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
... inequality ( i ) of Theorem 6 holds . Here the set S1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
Page 2190
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
Page 2403
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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