Some Results on Weakly Compact Positive Left Multipliers of a Certain Group Algebra

Let t be a weakly compact left multiplier on l∞0 (g) ∗. in this paper, we prove that if t is positive, then t maps l∞0 (g) ∗ into l1(g) and t is of the form φt for some positive function φ ∈ l1(g). using this result, we show that t = t + − t − for some positive weakly compact left multipliers t +, t − on l∞0 (g) ∗ if and only if t maps l∞0 (g) ∗ into l1(g)