Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 95
Page 1979
... shows that condition ( i ) of the theorem is satisfied . 8 COROLLARY . Every operator A in of spectral operators ... shows that A is a spectral operator . Now since it follows that e ( S ) xx for every x in H and thus that Ex → x for ...
... shows that condition ( i ) of the theorem is satisfied . 8 COROLLARY . Every operator A in of spectral operators ... shows that A is a spectral operator . Now since it follows that e ( S ) xx for every x in H and thus that Ex → x for ...
Page 2169
... shows that ( vi ) holds for every bounded Borel function ƒ 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 ƒ 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero