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Order and norm convergence in Banach lattices
Published online by Cambridge University Press: 18 May 2009
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Let(V, ≧, ‖ · ‖) be a Banach lattice, and denote V\{0} by V'. For the definition of a Banach lattice and other undefined terms used below, see Vulikh [4]. Leader [3] shows that, if norm convergence is equivalent to order convergence for sequences in V, then the norm is equivalent to an M-norm. By assuming the equivalence for nets in V we can strengthen this result.
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- Copyright © Glasgow Mathematical Journal Trust 1974
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