Linear Operators: Spectral operators |
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Page 1994
... converges , we see from the continuity of F that An❤ lim С | Xn ( s ) — Xm ( 8 ) | 2 ds = 0 , m.n∞ which implies ( III.3.6 ) that I converges in measure on σ . Conversely , if ( 29 ) and ( 30 ) hold , then , since the norms || = | n ...
... converges , we see from the continuity of F that An❤ lim С | Xn ( s ) — Xm ( 8 ) | 2 ds = 0 , m.n∞ which implies ( III.3.6 ) that I converges in measure on σ . Conversely , if ( 29 ) and ( 30 ) hold , then , since the norms || = | n ...
Page 2218
... converges weakly to a projection , then it converges strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra B is complete . Let { E } be a weakly convergent generalized sequence in B ...
... converges weakly to a projection , then it converges strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra B is complete . Let { E } be a weakly convergent generalized sequence in B ...
Page 2462
... converges uniformly to zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x ...
... converges uniformly to zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x ...
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