Linear Operators: Spectral operators |
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Page 1951
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF ...
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF ...
Page 1952
... Corollary 6 that NP + 1 = 0 and so T Q.E.D. is of finite type . 8 COROLLARY . If Tx = 0 , then Sx Nx = E ( o ) x = 0 if 0 ō . - ¢ PROOF . For a given x in X , the class of bounded linear operators in X for which Ax = 0 is a closed left ...
... Corollary 6 that NP + 1 = 0 and so T Q.E.D. is of finite type . 8 COROLLARY . If Tx = 0 , then Sx Nx = E ( o ) x = 0 if 0 ō . - ¢ PROOF . For a given x in X , the class of bounded linear operators in X for which Ax = 0 is a closed left ...
Page 2192
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
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