en عمومى General پژوهشي Research paper در این مقاله g-K-قابها را در فضای هیلبرت پرو C-*-مدولها معرفی و خواصشان را بررسی میکنیم. و نشان میدهیم تحت چه شرایطی خانواده ای از عملگرها g-K-قاب میباشند. بعلاوه G-سیستم های اتمی را معرفی و خواصشان را بررسی میکنیم. <div style="text-align: justify;">In this paper, the concept of K-g-frames in Hilbert pro-C^&lowast;-modules is introduced, and their basic properties are examined. The conditions under which family of operators can form a K-g-frame on Hilbert pro-C^&lowast;-modules are derived. Moreover g-atomic systems in Hilbert proC^&lowast;-modules are introduced and their properties are examined.</div> Hilbert modules over pro-C*-algebras, K-G-frames, Frame operators, Bounded module maps, G-atomic systems. 169 183 http://ijmsi.ir/browse.php?a_code=A-10-4954-1&slc_lang=en&sid=1 Akbar Nazari nazari@uk.ac.ir 100319475328460010228 100319475328460010228 No Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran Zahra Ahmadi Moosavi z-moosavi@math.uk.ac.ir 100319475328460010227 100319475328460010227 Yes Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran