This is an announcement for the paper "Schatten p-norm inequalities related to a characterization of inner product spaces" by O. Hirzallah, F. Kittaneh, and M. S. Moslehian. Abstract: Let $A_1, \cdots A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, \cdots A_n$ belong to a Schatten $p$-class, for some $p>0$, then \begin{equation*} 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. Moreover, \begin{equation*} \sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch. Archive classification: math.OA math.FA Mathematics Subject Classification: 46C15, 47A30, 47B10, 47B15 Remarks: 6 pages The source file(s), Schattenp-norminequalitiesrelatedtoacharacteriztionofinnerproductspaces.tex: 14968 bytes, is(are) stored in gzipped form as 0801.2726.gz with size 4kb. The corresponding postcript file has gzipped size 56kb. Submitted from: moslehian@ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2726 or http://arXiv.org/abs/0801.2726 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2726 or in gzipped form by using subject line get 0801.2726 to: math@arXiv.org.