Linear Operators, Part 2 |
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Page 2209
... uniformly closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed ...
... uniformly closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed ...
Page 2361
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in UN U1 . Since the set { U1 } , i ≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in UN U1 . Since the set { U1 } , i ≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
Page 2382
... uniformly for μe P + and 0 ≤t < ∞o . On the other hand , integrating by parts , we see that for each n [ TM a®e2tu ( s - t › qn ( s ) ds = — 1 1 00 In ( t ) - t 2iμ e21us - t ) q ( 8 ) dt → 0 2iμ as μ → ∞ , μ Є P + , uniformly in 0 ...
... uniformly for μe P + and 0 ≤t < ∞o . On the other hand , integrating by parts , we see that for each n [ TM a®e2tu ( s - t › qn ( s ) ds = — 1 1 00 In ( t ) - t 2iμ e21us - t ) q ( 8 ) dt → 0 2iμ as μ → ∞ , μ Є P + , uniformly in 0 ...
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