Linear Operators, Part 2 |
From inside the book
Results 1-3 of 30
Page 2082
... exercise , let x , xo , and σo σ 。 be chosen so that x * E ( oo ) x 。 0 and let g be the Radon - Nikodým deriva- tive of x * E ( ) x 。 with respect to μ . There is a subset o1 of oo on which g is bounded away from zero and we let = 1 ...
... exercise , let x , xo , and σo σ 。 be chosen so that x * E ( oo ) x 。 0 and let g be the Radon - Nikodým deriva- tive of x * E ( ) x 。 with respect to μ . There is a subset o1 of oo on which g is bounded away from zero and we let = 1 ...
Page 2172
... exercise and let op in ( l∞ ) * be a Banach limit as in Exercise II.4.22 . Let A be defined on l by Show that A2 Ax = A ( §1 , 2 , 3 , . . . ) = ( p ( x ) , 0 , 0 , ... ) . = = O and that p ( Tx ) = p ( x ) and AT TA . However , if σ ...
... exercise and let op in ( l∞ ) * be a Banach limit as in Exercise II.4.22 . Let A be defined on l by Show that A2 Ax = A ( §1 , 2 , 3 , . . . ) = ( p ( x ) , 0 , 0 , ... ) . = = O and that p ( Tx ) = p ( x ) and AT TA . However , if σ ...
Page 2489
... Exercise 17. ) H t ( a ) Show that the limit W + w = limt . Uw exists , and that there exist operators A , B of the ... Exercise 17. ) ( c ) ( Wave operator invariance theorem ) Show XX.5.19 2489 EXERCISES.
... Exercise 17. ) H t ( a ) Show that the limit W + w = limt . Uw exists , and that there exist operators A , B of the ... Exercise 17. ) ( c ) ( Wave operator invariance theorem ) Show XX.5.19 2489 EXERCISES.
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