Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 95
Page 1979
... shows that condition ( i ) of the theorem is satisfied . Q.E.D. 8 COROLLARY . Every operator A in AP is the strong ... shows that A is a spectral operator . Now since it follows that e ( S * ) x → → x for every x in 5 and thus that Ex ...
... shows that condition ( i ) of the theorem is satisfied . Q.E.D. 8 COROLLARY . Every operator A in AP is the strong ... shows that A is a spectral operator . Now since it follows that e ( S * ) x → → x for every x in 5 and thus that Ex ...
Page 2169
... shows that ( vi ) holds for every bounded Borel function f and every continuous function g . A repetition of this argument shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) ...
... shows that ( vi ) holds for every bounded Borel function f and every continuous function g . A repetition of this argument shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) ...
Page 2170
... shows that - | ( xI − T ) x | 2 = | I ( a ) x | 2 + | ( R ( x ) I − T ) x | 2 ≥ | J ( a ) | 2 | x | 2 , - so that | x | ≤ ( α1 - T ) x · T ) x \ . | I ( α ) | This shows that ( al - T ) -1 exists as a bounded operator , from which ...
... shows that - | ( xI − T ) x | 2 = | I ( a ) x | 2 + | ( R ( x ) I − T ) x | 2 ≥ | J ( a ) | 2 | x | 2 , - so that | x | ≤ ( α1 - T ) x · T ) x \ . | I ( α ) | This shows that ( al - T ) -1 exists as a bounded operator , from which ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
35 other sections not shown
Other editions - View all
Common terms and phrases
A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero