Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Results 1-3 of 81
Page 1947
... adjoint operator B in 5 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 . = 2 - = = - PROOF . For Ee B1 , put F ( E ) ...
... adjoint operator B in 5 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 . = 2 - = = - PROOF . For Ee B1 , put F ( E ) ...
Page 2169
... operator E ( o ) defined by ( iv ) is a bounded spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert ...
... operator E ( o ) defined by ( iv ) is a bounded spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert ...
Page 2481
... adjoint operator , and that if fe D ( T1 ( ) ) is a function in its domain , then af / or , and o2f / dx , dx , are ... operator , and that , as λ → ∞ , T1 ( 71 ) ( T1 ( V ) + ) - 1 converges uniformly to zero . ( c ) Show , under the ...
... adjoint operator , and that if fe D ( T1 ( ) ) is a function in its domain , then af / or , and o2f / dx , dx , are ... operator , and that , as λ → ∞ , T1 ( 71 ) ( T1 ( V ) + ) - 1 converges uniformly to zero . ( c ) Show , under the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero