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 ) λK ≤ K for all λ € 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 ) λK ≤ K for all λ € R , A≥0 , and ( iii ) K ^ ( −K ) = { 0 } . Conversely , if K is a subset of V satis- fying ( i ) , ( ii ) ...
Page 2500
... positive for almost all A if H2 — H1 is a positive operator , or more generally if there exists a Hermitian operator To with finite range such that H2 - H1 + To is positive . Similar results are proved by Birman and Krein for a pair U2 ...
... positive for almost all A if H2 — H1 is a positive operator , or more generally if there exists a Hermitian operator To with finite range such that H2 - H1 + To is positive . Similar results are proved by Birman and Krein for a pair U2 ...
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 ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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