Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 86
Page 1956
... follows from Theorem 2 that A is in the point spectrum of T. If E ( { λ } ) = 0 then it follows from Theorem 2 that I T is one - to - one . By Corollary 7.12 the set ( AI – T ) X is dense in X and hence A is in the continuous spectrum ...
... follows from Theorem 2 that A is in the point spectrum of T. If E ( { λ } ) = 0 then it follows from Theorem 2 that I T is one - to - one . By Corollary 7.12 the set ( AI – T ) X is dense in X and hence A is in the continuous spectrum ...
Page 2246
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin C ) ... follows that ( sin #C ) ˆP ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin C ) ... follows that ( sin #C ) ˆP ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
Page 2459
... follows at once . If xn € Σac ( H ) and lim∞ = x , then , by what we have already proved , we may write x = y1 + y2 + ys , where y1 E Zac ( H ) and yY2 , Yз are orthogonal to Σac ( H ) . But , since x , € Σac ( H ) we have ( în , y ) ...
... follows at once . If xn € Σac ( H ) and lim∞ = x , then , by what we have already proved , we may write x = y1 + y2 + ys , where y1 E Zac ( H ) and yY2 , Yз are orthogonal to Σac ( H ) . But , since x , € Σac ( H ) we have ( în , y ) ...
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