Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 93
Page 2174
... hence is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ... Hence we have lett ( S + T ) | = | ettsettT | ≤ | etts || ettT | ≤ M1M1⁄2 for all te R. Hence if this boundedness ...
... hence is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ... Hence we have lett ( S + T ) | = | ettsettT | ≤ | etts || ettT | ≤ M1M1⁄2 for all te R. Hence if this boundedness ...
Page 2312
... hence for all y in the closure of the range of T. On the other hand , if y is not in the closure of the range of T ... hence closed by Corollary IV.3.2 . Hence it suffices to show that the second of the direct summands is closed . By VII ...
... hence for all y in the closure of the range of T. On the other hand , if y is not in the closure of the range of T ... hence closed by Corollary IV.3.2 . Hence it suffices to show that the second of the direct summands is closed . By VII ...
Page 2357
... Hence = -V V ( P + N ) ( S – XI ) ̄ ” — P ( S — \ I ) − ' + N ( S — \ I ) − " = P ( TMI ) - ' L + N ( S – XI ) - " = is a bounded operator which is compact if P ( T — XI ) - ' is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) ...
... Hence = -V V ( P + N ) ( S – XI ) ̄ ” — P ( S — \ I ) − ' + N ( S — \ I ) − " = P ( TMI ) - ' L + N ( S – XI ) - " = is a bounded operator which is compact if P ( T — XI ) - ' is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) ...
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