Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 85
Page 1951
... compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF . By Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is ...
... compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF . By Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is ...
Page 2364
... compact by Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for | n | < 1 + d1 . It follows from Lemma VII.6.6 that if O is any bounded open set whose ...
... compact by Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for | n | < 1 + d1 . It follows from Lemma VII.6.6 that if O is any bounded open set whose ...
Page 2462
Nelson Dunford, Jacob T. Schwartz. = is compact . Put CQR1 , and D R2 , so that VCD . The operator C is compact by Corollary VI.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and ...
Nelson Dunford, Jacob T. Schwartz. = is compact . Put CQR1 , and D R2 , so that VCD . The operator C is compact by Corollary VI.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and ...
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