Linear Operators: Spectral operators |
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Page 2154
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that ( T_ \ I ) n + 1 + { x | ( T − AI ) n + xx = 0 } is dense in X. By induction , it is seen that the manifold . ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } ...
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that ( T_ \ I ) n + 1 + { x | ( T − AI ) n + xx = 0 } is dense in X. By induction , it is seen that the manifold . ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } ...
Page 2214
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra A ( B ) generated by B. Thus W ( B ) ≤ A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra A ( B ) generated by B. Thus W ( B ) ≤ A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
Page 2270
... manifold in X * containing all the sets A .. ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
... manifold in X * containing all the sets A .. ( b ) The projection Fo with range M and null manifold N defined by this decomposition belongs to D. It is easily verified that X - completeness implies completeness for D as an abstract ...
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