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Published online by Cambridge University Press: 22 January 2016
This is a continuation of the author’s previous work [0-6], in which we have settled a conjecture of Cheeger-Goresky-MacPherson [C-G-M] by proving that the L2 cohomology group of a compact (reduced) complex space is canonically isomorphic to its (middle) intersection cohomology group. Our aim here is, in addition to that result, to extend further the classical L2 harmonic theory to complex spaces with arbitrary singularities by establishing the following.