Linear Operators: Spectral operators |
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Page 1951
... linear subspace of X , then the set of bounded linear operators A in X for which AX≤ Y is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ...
... linear subspace of X , then the set of bounded linear operators A in X for which AX≤ Y is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ...
Page 1960
... linear map A : x → y of HP into itself , it is easy to define a set a ,, of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in Ho and let H , be ...
... linear map A : x → y of HP into itself , it is easy to define a set a ,, of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in Ho and let H , be ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
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