Linear Operators, Part 2 |
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Page 2068
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space L。= L1 L1 satisfies ( 11 ) . More ...
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space L。= L1 L1 satisfies ( 11 ) . More ...
Page 2112
... satisfies the condition : ( α ) N ( F1 , T ) ≤ M ( F2 , T ) , 1 if F , the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X ...
... satisfies the condition : ( α ) N ( F1 , T ) ≤ M ( F2 , T ) , 1 if F , the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X ...
Page 2314
... satisfies the boundary condition at t = 0 if tan sa = kos , and satisfies the boundary conditions at t = 1 if tan 8 ( 1 + x ) = k18 . Thus , using the addition formula for the tangent function , TX can only fail to have an inverse if λ ...
... satisfies the boundary condition at t = 0 if tan sa = kos , and satisfies the boundary conditions at t = 1 if tan 8 ( 1 + x ) = k18 . Thus , using the addition formula for the tangent function , TX can only fail to have an inverse if λ ...
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