The space $LG'$ of generalized functions, whose elements have a Laguerre orthonormal expansion into a series, are investigated in [2] and [3] . In this paper we define the space $LG$ by using a suitable family of seminorms. This implies some properties of the space $LG'$ and the representation theorem for some elements from $LG'$. Also, by using a convolution in $LG'$ and a Laplace transform we give expansions into a series of same important generalized functions from $LG'$.