Linear Operators, Part 2 |
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Page 2148
... consequently λ is in p ( T ) , which means that XI — T is a one - to - one map of E ( o ) X into all of itself . Since o do ( T ) , we have E ( o ) E ( So ( T ) ) = E ( S ) and consequently E ( S ) X is an invariant subspace of E ( o ) ...
... consequently λ is in p ( T ) , which means that XI — T is a one - to - one map of E ( o ) X into all of itself . Since o do ( T ) , we have E ( o ) E ( So ( T ) ) = E ( S ) and consequently E ( S ) X is an invariant subspace of E ( o ) ...
Page 2243
... Consequently , the limit f1 ( T ) x = lim , → ∞ ƒ ( T | E ( en ) X ) E ( en ) x exists and equals ƒf2 ( T ) x . Thus , by Theorem 11 , for each x in D ( ƒ1⁄2 ( T ) ) , fi ( T ) E ( cm ) x = fz ( T ) E ( cm ) x = E ( cm ) f2 ( T ) x ...
... Consequently , the limit f1 ( T ) x = lim , → ∞ ƒ ( T | E ( en ) X ) E ( en ) x exists and equals ƒf2 ( T ) x . Thus , by Theorem 11 , for each x in D ( ƒ1⁄2 ( T ) ) , fi ( T ) E ( cm ) x = fz ( T ) E ( cm ) x = E ( cm ) f2 ( T ) x ...
Page 2343
... Consequently , Hypothesis 1 is satisfied and the constant ẞ of formula ( 16 ) is zero . The conclusion of Theorem 8 is consequently valid in all cases in which n = 2v is even and the boundary values ( 1 ) may be separated into a set of ...
... Consequently , Hypothesis 1 is satisfied and the constant ẞ of formula ( 16 ) is zero . The conclusion of Theorem 8 is consequently valid in all cases in which n = 2v is even and the boundary values ( 1 ) may be separated into a set of ...
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