Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 84
Page 1991
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
Page 2066
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping q : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping q : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
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