Linear Operators, Part 2 |
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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 ) λK ≤ K for all λ € R , ≥ ≥ 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 ) λK ≤ K for all λ € R , ≥ ≥ 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 Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero