Linear Operators, Part 2 |
From inside the book
Results 1-3 of 56
Page 1951
... statement follows . Q.E.D. If is a closed linear subspace of X , then the set of bounded linear operators A in X for which AX ≤ is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 ...
... statement follows . Q.E.D. If is a closed linear subspace of X , then the set of bounded linear operators A in X for which AX ≤ is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 ...
Page 2236
... statement ( v ) remains to be proved . In the first case described in statement ( v ) , σ ( T ) is a compact subset of U , and by Corollary XV.3.5 , E ( σ ( T ) ) = I so that without loss of generality each of the sets e ,, n ≥ 1 , may ...
... statement ( v ) remains to be proved . In the first case described in statement ( v ) , σ ( T ) is a compact subset of U , and by Corollary XV.3.5 , E ( σ ( T ) ) = I so that without loss of generality each of the sets e ,, n ≥ 1 , may ...
Page 2239
... Statement ( d ) is obvious . Letting e e 。 and x = E ( e ) X , we have T ( fxe ) x = lim T ( fxe ) E ( en ) x = lim ... Statement ( a ) clearly will follow from statement ( b ) . Statement ( b ) follows from statement ( f ) ; indeed ...
... Statement ( d ) is obvious . Letting e e 。 and x = E ( e ) X , we have T ( fxe ) x = lim T ( fxe ) E ( en ) x = lim ... Statement ( a ) clearly will follow from statement ( b ) . Statement ( b ) follows from statement ( f ) ; indeed ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero