Linear Operators, Part 2 |
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Page 1974
... implies ( iii ) . It is clear that ( iii ) implies ( i ) , and so to prove the lemma it will suffice to prove that ( i ) implies ( ii ) . Let ( a ) sup e - ess sup E ( o ; F ( s ) ) ] = K < ∞ , σε SEG i and suppose that for some i GS ...
... implies ( iii ) . It is clear that ( iii ) implies ( i ) , and so to prove the lemma it will suffice to prove that ( i ) implies ( ii ) . Let ( a ) sup e - ess sup E ( o ; F ( s ) ) ] = K < ∞ , σε SEG i and suppose that for some i GS ...
Page 2174
... implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's ... imply that T is spectral , even when X is reflexive . To see this , note that if S and T are commuting scalar operators ...
... implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's ... imply that T is spectral , even when X is reflexive . To see this , note that if S and T are commuting scalar operators ...
Page 2266
... implies Ea 0 implies E = 0 as noted in Defini- tion 4. Thus the carrier of any vector belongs to C. α α B It will next be shown that C is a dense ideal . If E € B , then it bounds the carrier projection of every vector in its range . By ...
... implies Ea 0 implies E = 0 as noted in Defini- tion 4. Thus the carrier of any vector belongs to C. α α B It will next be shown that C is a dense ideal . If E € B , then it bounds the carrier projection of every vector in its range . By ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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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