%0 Journal Article %T G-frames and Hilbert-Schmidt operators %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Abdollahpour, M. R. %A Najati, A. %D 2011 %\ 12/15/2011 %V 37 %N No. 4 %P 141-155 %! G-frames and Hilbert-Schmidt operators %K frame %K g-frame %K Besselian g-frame %K alpha-dual %K Hilbert-Schmidt operator %R %X In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space. %U http://bims.iranjournals.ir/article_376_dec38006d54dac2838992a1a939b821a.pdf