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 σ - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean ...
... projections in a σ - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean ...
Page 2300
... projections E ( λ , ; 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 , - , ( E ( A ; T ) — E ( μn ; T + P ) ) clearly ...
... projections E ( λ , ; 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 , - , ( E ( A ; T ) — E ( μn ; T + P ) ) clearly ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero