Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 67
Page 2094
... subspace X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T of T to is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
... subspace X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T of T to is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
Page 2113
... subspace spectral maximal subspace of Te B ( X ) if ( i ) ( ii ) if 3 is a closed linear subspace of X which is invariant under T and o ( T3 ) o ( TV ) , then 3. ( See also Ljubič and Macaev [ 2 ; §4 , IV ] . ) It can be shown that if ...
... subspace spectral maximal subspace of Te B ( X ) if ( i ) ( ii ) if 3 is a closed linear subspace of X which is invariant under T and o ( T3 ) o ( TV ) , then 3. ( See also Ljubič and Macaev [ 2 ; §4 , IV ] . ) It can be shown that if ...
Page 2114
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
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