Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 93
Page 1930
... spectral set for the operator T to be any set 8 for which So ( T ) is open and closed in o ( T ) and if for each 8 in the field of spectral sets we define the projection E ( 8 ) by the formula E ( S ) 1 2 i √ R ( A ; T ) dλ , C where C ...
... spectral set for the operator T to be any set 8 for which So ( T ) is open and closed in o ( T ) and if for each 8 in the field of spectral sets we define the projection E ( 8 ) by the formula E ( S ) 1 2 i √ R ( A ; T ) dλ , C where C ...
Page 2150
... spectrum is totally disconnected , every spectral point is contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( ...
... spectrum is totally disconnected , every spectral point is contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( ...
Page 2256
... spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral ...
... spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
36 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 follows from Theorem 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