Notes on the unconditional convergence of multidimensional functional series.

Bareladze, G.

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The paper is devoted to some problems concerning a convergence of pointwise type in the $L_{2}$ -space over a von Neumann algebra M with a faithful normal state Φ [3]. Here $L_{2} = L_{2} (M, Φ)$ is the completion of M under the norm ${x \to | x |}^{2} = Φ {(x * x)}^{1 / 2}$ .