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On the convergence of
resolvents of operators
Minoru Hasegawa |
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Vol. 21 (1967), No. 1, 35–47
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Abstract |
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Let a family of linear operators {An}(n = 1,2,⋯) in a Banach space X have the resolvents {R(λ;An)} which is equicontinuous in n. Suppose that {An} is a Cauchy sequence on a dense set. Then the question of convergence arises; when will {R(λ;An)x} be a Cauchy sequence for all x ∈ X? This problem is treated in some special cases and an application to the following theorem is presented. Let A be the generator of a positive contraction semigroup ∑ and let B be a linear operator with domain 𝒟(B) ⊃𝒟(A) in a weakly complete Banach lattice X. Then A + B or its closed extension generates a positive contraction semi-group Σ′ which dominates Σ if and only if A + B is dissipative and B is positive. |
Mathematical Subject Classification
Primary: 47.50
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Milestones
Received: 27 October 1965
Published: 1 April 1967
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Authors |
| Minoru Hasegawa | |
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