Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2256
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. - 1 PROOF . Suppose first ... zero is contained in an arbitrarily small compact set open in the relative topology of σ ( R ) . - Suppose now that U ...
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. - 1 PROOF . Suppose first ... zero is contained in an arbitrarily small compact set open in the relative topology of σ ( R ) . - Suppose now that U ...
Page 2325
... zero of sin ( z — a ) = ß . Put R R ( 1 ) + 2mπ , R2 ) R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + a + 22 , 21 # 22 , 2π > Rz1 Rz20 of the zeros of sin ( z — a ) — ẞ , we wish to show that for m sufficiently ...
... zero of sin ( z — a ) = ß . Put R R ( 1 ) + 2mπ , R2 ) R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + a + 22 , 21 # 22 , 2π > Rz1 Rz20 of the zeros of sin ( z — a ) — ẞ , we wish to show that for m sufficiently ...
Page 2462
... zero and { CT * } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . PROOF . The set K = C ( { xe || x | ≤ 1 } ) is ...
... zero and { CT * } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . PROOF . The set K = C ( { xe || x | ≤ 1 } ) is ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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