Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 77
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 2461
... positive square root ( V * V ) 1 / 2 of the bounded self adjoint operator V * V . As is observed in the first ... positive eigenvalues of R , arranged in decreasing order and repeated according to multiplicity , are μ1 , μ2 , ... , then ...
... positive square root ( V * V ) 1 / 2 of the bounded self adjoint operator V * V . As is observed in the first ... positive eigenvalues of R , arranged in decreasing order and repeated according to multiplicity , are μ1 , μ2 , ... , then ...
Page 2564
... positive operators . Sci . Papers College Gen. Ed . Univ . Tokyo 14 , 181–182 ( 1964 ) . 2 . 3 . On spectral properties of some positive operators . Natur . Sci . Rep . Ochanomizu Univ . 15 , 53-64 ( 1964 ) . On spectral properties of ...
... positive operators . Sci . Papers College Gen. Ed . Univ . Tokyo 14 , 181–182 ( 1964 ) . 2 . 3 . On spectral properties of some positive operators . Natur . Sci . Rep . Ochanomizu Univ . 15 , 53-64 ( 1964 ) . On spectral properties of ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero