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On some isomorphism on the category of \(b\)-spaces. (Russian, English) Zbl 1033.46057

Sib. Mat. Zh. 44, No. 5, 961-971 (2003); translation in Sib. Math. J. 44, No. 5, 749-756 (2003).
Summary: Given a nuclear \(b\)-space \(N\), we show that if \(\Omega\) is a finite or \(\sigma\)-finite measure space and \(1\leq p\leq\infty\), then the functors \(L_{\text{loc}}^p (\Omega,N\varepsilon\cdot)\) and \(N\varepsilon L^p(\Omega,\cdot)\) are isomorphic on the category of \(b\)-spaces of L. Waelbroeck.

MSC:

46M15 Categories, functors in functional analysis
46A40 Ordered topological linear spaces, vector lattices
46M05 Tensor products in functional analysis
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