Linear Operators, Part 2 |
From inside the book
Results 1-3 of 72
Page 2397
... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11. Hypothesis ( ii ) has been established and is given by Lemma 7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII ...
... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11. Hypothesis ( ii ) has been established and is given by Lemma 7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII ...
Page 2401
... hypothesis ( b ) , to Using hypothesis ( c ) , we may write this last equation as ( 5 ) q ( B — 4 ( B , A1 ) ) = q ( A1 ) . Now , by hypothesis , the map B → ↓ ( B , A1 ) of A → A has norm at most M2 ( M1 + M2 ) 1 . Thus , by Lemma ...
... hypothesis ( b ) , to Using hypothesis ( c ) , we may write this last equation as ( 5 ) q ( B — 4 ( B , A1 ) ) = q ( A1 ) . Now , by hypothesis , the map B → ↓ ( B , A1 ) of A → A has norm at most M2 ( M1 + M2 ) 1 . Thus , by Lemma ...
Page 2449
... hypothesis , 6M2t , ≤ 1 , we have tn + 12t1 and our assertion follows . It also follows from ( 5 ) and hypotheses ( d ) and ( e ) that ( 7 ) ||| A ( n + 1 ) — A ( n ) ||| ( n - 1 ) ≤ M2 ( || AŽn ||| + ||| AŽ − 1 ||| + ||| A1 ...
... hypothesis , 6M2t , ≤ 1 , we have tn + 12t1 and our assertion follows . It also follows from ( 5 ) and hypotheses ( d ) and ( e ) that ( 7 ) ||| A ( n + 1 ) — A ( n ) ||| ( n - 1 ) ≤ M2 ( || AŽn ||| + ||| AŽ − 1 ||| + ||| A1 ...
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