Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 61
Page 1967
... inverse in Y has this inverse also in X. e = = - = - -1 PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so ee * = ( ee * ) * = e ** e * = ee * e * . Now let x in X have the inverse x in . Then ( x - 1 ) * x ...
... inverse in Y has this inverse also in X. e = = - = - -1 PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so ee * = ( ee * ) * = e ** e * = ee * e * . Now let x in X have the inverse x in . Then ( x - 1 ) * x ...
Page 2065
... inverse in A if â ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those ...
... inverse in A if â ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those ...
Page 2069
... inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in " and the determinant & = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
... inverses . Then Ag contains all inverses . 1 PROOF . If the operator A in Ag has an inverse in B ( 5 " ) then , by Corollary 9.6 , A - 1 is in " and the determinant & = det ( a ,, ) has an inverse in A. Since A。 contains all inverses ...
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