Linear Operators: Spectral operators |
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Page 1928
... projections A and B in are the projections AB and A + B- AB , respectively . The ranges of the inter- section and union of two commuting projections are given by the equa- tions ( A ^ \ B ) X = ( AX ) ~ ( BX ) , ( A \ B ) ( X ) = ( AX ) ...
... projections A and B in are the projections AB and A + B- AB , respectively . The ranges of the inter- section and union of two commuting projections are given by the equa- tions ( A ^ \ B ) X = ( AX ) ~ ( BX ) , ( A \ B ) ( X ) = ( AX ) ...
Page 2218
... projections in a o - complete Boolean algebra of projections in a B - space 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 ...
... projections in a o - complete Boolean algebra of projections in a B - space 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 ...
Page 2300
... projections E ( A ,; T ) is uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) – E ( μn ; T + P ) ) clearly ...
... projections E ( A ,; T ) is uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) – E ( μn ; T + P ) ) clearly ...
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