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 1 2 | ett ( s + T ) | = | ettsettт | ≤etts || et | ≤ M1M2 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 1 2 | ett ( s + T ) | = | ettsettт | ≤etts || et | ≤ M1M2 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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero