Linear Operators: Spectral operators |
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Page 1947
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... : Bk . - 1 - PROOF . For Ee B1 , put F ( E ) = I ...
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... : Bk . - 1 - PROOF . For Ee B1 , put F ( E ) = I ...
Page 2460
... adjoint operator in sing ( H ) , and that H | ( Σ , ( H ) ~ D ( H ) ) is a densely defined self adjoint operator in Σ , ( H ) ; details are left to the reader . Statement ( c ) of the present lemma follows at once . j = 1 = = Finally ...
... adjoint operator in sing ( H ) , and that H | ( Σ , ( H ) ~ D ( H ) ) is a densely defined self adjoint operator in Σ , ( H ) ; details are left to the reader . Statement ( c ) of the present lemma follows at once . j = 1 = = Finally ...
Page 2481
... adjoint operator , and that if ƒ e D ( T1 ( V ) ) is a function in its domain , then af / ax , and o2f / dx , dx ... operator , and that , as → ∞ , T1 ( T1 ) ( T1 ( P ) + ) - 1 converges uniformly to zero . 1 ( c ) Show , under the ...
... adjoint operator , and that if ƒ e D ( T1 ( V ) ) is a function in its domain , then af / ax , and o2f / dx , dx ... operator , and that , as → ∞ , T1 ( T1 ) ( T1 ( P ) + ) - 1 converges uniformly to zero . 1 ( c ) Show , under the ...
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