Linear Operators, Part 2 |
From inside the book
Results 1-3 of 90
Page 1962
... linear functional x * on Ho determines p linear functionals x * , ding to the relations ( 9 ) x * x1 = x * H ̧1x1 , " ... " P x1 EH , x * on H accor- and , conversely , any set x1 , x of p linear functionals uniquely deter- mines a ...
... linear functional x * on Ho determines p linear functionals x * , ding to the relations ( 9 ) x * x1 = x * H ̧1x1 , " ... " P x1 EH , x * on H accor- and , conversely , any set x1 , x of p linear functionals uniquely deter- mines a ...
Page 2066
... linear functional on L1 determined by the relation h ( g ) = x * g for every g in L1 . Then , since the vector valued function f is continuous and bounded as a map from RN into L1 , the vector valued function fig ( t ) is integrable in ...
... linear functional on L1 determined by the relation h ( g ) = x * g for every g in L1 . Then , since the vector valued function f is continuous and bounded as a map from RN into L1 , the vector valued function fig ( t ) is integrable in ...
Page 2205
... linear functional x * in X * with the properties ( i ) x * Ex 。≥0 , Ee B ; ( ii ) if x * Ex 。= 0 for some E in B , then Ex 。= 0 . PROOF . By Corollary 10 , B is the range of a countably additive spectral measure E defined on a o ...
... linear functional x * in X * with the properties ( i ) x * Ex 。≥0 , Ee B ; ( ii ) if x * Ex 。= 0 for some E in B , then Ex 。= 0 . PROOF . By Corollary 10 , B is the range of a countably additive spectral measure E defined on a o ...
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