Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2017.467.474KhanVakeel AhmadRababahRami K.A.EsiAyhanAbdullahSameera Ameen AliAlshloolKamal Mohammed Ali Suleiman92017179Background and Objective: This study comes from the notion of I-convergence which is the generalization of statistical convergence. The idea of I-convergent sequence spaces was motivated by the statistical convergence for double sequence. The I-convergence for double sequence in real line and general metric space. Methodology: This has motivated us to study the ideal convergence for double sequences using compact operator and define these spaces , and . Further, inclusion relations between these spaces and some properties such as solidity and monotonic was investigated. Results: This study consists of two sections. In the first section, it was given the basic definitions related to double sequences, compact operator, ideal, filter etc. The second section deals with the main results like , and are linear spaces and normed spaces. It was defined a real valued function on as h(x) = I-lim x and proved that this function is Lipschitz continuous and hence uniformly continuous. At the last, topological properties of these spaces like monotonicity and solidity are discussed. Conclusion: This study has used compact linear operator to define spaces of ideal convergent double sequence , and which provide better tool to study a more general spaces of sequences.]]>Fast, H.,1951Steinhaus, H.,1951Fridy, J.A.,1985Salat, T.,1980Tripath, B.C.,1998Mursaleen and O.H.H. Edely,2003Kostyrko, P., W. Wilczynski and T. Salat,2000Kostyrko, P., M. Macij, T. Salat and M. Sleziak,2005Salat, T., B.C. Tripathy and M. Ziman,2004Tripathy, B. and B. Hazarika,2009Tripathy, B.C. and B. Hazarika,2011Das, P., P. Kostyrko, W. Wilczynski and P. Malik,2008Pringsheim, A.,1900Kreyszig, E.,1978Maddox, I.G.,1988Basar, F. and B. Altay,2003Sengonul, M.,2007Salat, T., B.C. Tripathy and M. Ziman,2005Mursaleen and O.H.H. Edely,2003Khan, V.A. and K. Ebadullah,2011Khan, V.A., K. Ebadullah and Y. Aligarh,2014Khan, V.A., M. Shafiq and R.K.A. Rababah,2015Khan, V.A., M. Shafiq, R.K.A. Rababah and A. Esi,2016Khan, V.A., Yasmeen, H. Fatima, H. Altaf and Q.D. Lohani,2016Khan, V.A., Y. Khan, H. Altaf, A. Esi and A. Ahamd,2017Khan, V.A., H. Fatima, A. Esi, S.A. Abdullah and K.M.A.S. Alshlool,2017