Linear Operators, Part 2 |
From inside the book
Results 1-3 of 69
Page 2150
... contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( T ) set , condition ( D ) is im- mediate . let To ...
... contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( T ) set , condition ( D ) is im- mediate . let To ...
Page 2156
... contained in y and σ ( 22 ) is contained in the complement y ' . — Actually more will be proved , for it will be shown that z1 and z2 may be chosen so that z , + z2 is arbitrarily close to y and the spectra o ( 21 ) , o ( 22 ) are contained ...
... contained in y and σ ( 22 ) is contained in the complement y ' . — Actually more will be proved , for it will be shown that z1 and z2 may be chosen so that z , + z2 is arbitrarily close to y and the spectra o ( 21 ) , o ( 22 ) are contained ...
Page 2234
... contained in U , it may be supposed , since f ( T ) is independent of { e } , that e = e1 . If x is in E ( e ) , then , by the paragraph preceding Definition 8 , f ( T | E ( en ) X ) x = f ( T | E ( e ) X ) x for n ≥1 so that f ( T ) x ...
... contained in U , it may be supposed , since f ( T ) is independent of { e } , that e = e1 . If x is in E ( e ) , then , by the paragraph preceding Definition 8 , f ( T | E ( en ) X ) x = f ( T | E ( e ) X ) x for n ≥1 so that f ( T ) x ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 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 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