Linear Operators: Spectral operators |
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Page 2068
... satisfies ( 11 ) . Also the space LoL1C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L1 L1 satisfies ( 11 ) . More generally ...
... satisfies ( 11 ) . Also the space LoL1C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L1 L1 satisfies ( 11 ) . More generally ...
Page 2112
... satisfies the condition : ( α ) N ( F1 , T ) ≤ M ( F2 , T ′ ) , 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 ′ ) , 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 s ( 1 + x ) = k18 . Thus , using the addition formula for the tangent function , T – λ can only fail to have an inverse if ...
... satisfies the boundary condition at t = 0 if tan sa = kos , and satisfies the boundary conditions at t = 1 if tan s ( 1 + x ) = k18 . Thus , using the addition formula for the tangent function , T – λ can only fail to have an inverse if ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero