Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 49
Page 2265
... disjoint elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \ / \ / En · ( ii ) If En ‡ 0 , E , has uniform multiplicity n . Ꮐ PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform ...
... disjoint elements in B , n running over the cardinals ≤m ( I ) , such that ( i ) I = \ / \ / En · ( ii ) If En ‡ 0 , E , has uniform multiplicity n . Ꮐ PROOF . We show first that each nonzero E B bounds a nonzero Ge B of uniform ...
Page 2266
... disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying this condition . It will be shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 ...
... disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying this condition . It will be shown that is a dense σ - ideal in B and thus , in defining the multiplicity on B , Lemma 2 ...
Page 2267
... disjoint projections E , each of which is the carrier of a vector x with | x | ≤ 1. Define x 。== 12- " x . Clearly ... disjoint elements in such that each G is bounded by some Eak and EoV - 1 G. For we may consider families of disjoint ...
... disjoint projections E , each of which is the carrier of a vector x with | x | ≤ 1. Define x 。== 12- " x . Clearly ... disjoint elements in such that each G is bounded by some Eak and EoV - 1 G. For we may consider families of disjoint ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
36 other sections not shown
Other editions - View all
Common terms and phrases
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 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