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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Page 2130
... positive cone of V ( with respect to ≤ ) ; it is easy to see that K satisfies ( i ) K + K ≤ K , ( ii ) AK ≤ K for all λe R , A≥0 , and ( iii ) K ~ ( −K ) = { 0 } . Conversely , if K is a subset of V satis- fying ( i ) , ( ii ) ...
... positive cone of V ( with respect to ≤ ) ; it is easy to see that K satisfies ( i ) K + K ≤ K , ( ii ) AK ≤ K for all λe R , A≥0 , and ( iii ) K ~ ( −K ) = { 0 } . Conversely , if K is a subset of V satis- fying ( i ) , ( ii ) ...
Page 2564
... positive operators . Sci . Papers College Gen. Ed . Univ . Tokyo 14 , 181–182 ( 1964 ) . 2 . On spectral properties of some positive operators . Natur . Sci . Rep . Ochanomizu Univ . 15 , 53-64 ( 1964 ) . 3. On spectral properties of ...
... positive operators . Sci . Papers College Gen. Ed . Univ . Tokyo 14 , 181–182 ( 1964 ) . 2 . On spectral properties of some positive operators . Natur . Sci . Rep . Ochanomizu Univ . 15 , 53-64 ( 1964 ) . 3. On spectral properties of ...
Page 2565
... positive operators in C ( X ) , I , II . I. Illinois J. Math . 11 , 703-715 ( 1967 ) . II . ibid . 12 , 525-538 ( 1968 ) Banach lattices and positive operators . Springer - Verlag ( to appear ) . Schaefer , H. H. , and Walsh , B. J. 1 ...
... positive operators in C ( X ) , I , II . I. Illinois J. Math . 11 , 703-715 ( 1967 ) . II . ibid . 12 , 525-538 ( 1968 ) Banach lattices and positive operators . Springer - Verlag ( to appear ) . Schaefer , H. H. , and Walsh , B. J. 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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