Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 93
Page 1953
Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 11
COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is the only bounded linear
operator for which either AT = ( or TA = 0 . PROOF . If either AT = 0 or TA = 0 then
, by ...
Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 11
COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is the only bounded linear
operator for which either AT = ( or TA = 0 . PROOF . If either AT = 0 or TA = 0 then
, by ...
Page 2137
Even though ( A ) is taken as a standing assumption throughout this section , it
will be indicated parenthetically in the statement of each lemma in the proof of
which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are
vectors in ...
Even though ( A ) is taken as a standing assumption throughout this section , it
will be indicated parenthetically in the statement of each lemma in the proof of
which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are
vectors in ...
Page 2218
PROOF . Since a spectral operator of scalar type is clearly in the weakly closed
algebra A generated by the projections in its resolution of the identity , it suffices
to show that every operator in A is a spectral operator of scalar type . This follows
...
PROOF . Since a spectral operator of scalar type is clearly in the weakly closed
algebra A generated by the projections in its resolution of the identity , it suffices
to show that every operator in A is a spectral operator of scalar type . This follows
...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Part | 1950 |
Copyright | |
9 other sections not shown
Other editions - View all
Common terms and phrases
adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero