Linear Operators: Spectral operators |
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Page 1951
... compact , then so are S , N , and every projection E ( o ) with 0 ¢ ō . PROOF . By Corollary VI.4.6 the weakly compact operators form a closed two - sided ideal in B ( X ) , from which the present statement follows . Q.E.D. If is a ...
... compact , then so are S , N , and every projection E ( o ) with 0 ¢ ō . PROOF . By Corollary VI.4.6 the weakly compact operators form a closed two - sided ideal in B ( X ) , from which the present statement follows . Q.E.D. If is a ...
Page 2081
... weakly compact if and only if it is compact . ( The same result holds for S in L1 over a positive measure space . ) 49 ( McCarthy ) Let E be a spectral measure XV.15.43 2081 EXERCISES.
... weakly compact if and only if it is compact . ( The same result holds for S in L1 over a positive measure space . ) 49 ( McCarthy ) Let E be a spectral measure XV.15.43 2081 EXERCISES.
Page 2186
... weakly complete space is weakly compact ( cf. VI.7.6 ) , it is seen from Theorem VI.7.3 that the map f → S ( f ) x uniquely determines a regular X - valued measure v ( · , x ) such that ( i ) S ( ƒ ) x = √ ƒ ( \ ) v ( d ) , x ) , fe C ...
... weakly complete space is weakly compact ( cf. VI.7.6 ) , it is seen from Theorem VI.7.3 that the map f → S ( f ) x uniquely determines a regular X - valued measure v ( · , x ) such that ( i ) S ( ƒ ) x = √ ƒ ( \ ) v ( d ) , x ) , fe C ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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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