پایایی دوگان‌ها و دوگان‌های تقریبی قاب‌ها و قاب‌های تعمیم‌یافته تحت عملگرهای کران‌دار

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی، دانشکده علوم پایه، دانشگاه قم، قم، ایران

چکیده

در این مقاله، پایایی دوگا‏ن‌ها و دوگان‌های تقریبی قاب‌های گسسته، قاب‌های پیوسته و قاب‌های تعمیم‌یافته در فضاهای هیلبرت و*C-مدول‌های هیلبرت تحت عملگرهای کران‌دار مورد توجه قرار می‌گیرد. نشان داده می‌شود که با برقراری برخی از شرایط، دوگا‏ن‌ها و دوگان‌های تقریبی تحت عملگرهای کران‌دار پایا هستند. به‌ویژه، پایایی دوگا‏ن‌ها و دوگان‌های تقریبی تحت ریخت‌های *C-مدول‌های هیلبرت، مورد مطالعه قرار می‌گیرد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The stability of duals and approximate duals of frames and generalized frames under the action of bounded operators

نویسنده [English]

  • Morteza Mirzaee Azandaryani
Department of Mathematics, University of Qom, Qom, Iran
چکیده [English]

In this paper, the stability of duals and approximate duals of discrete frames, continuous frames and generalized frames in Hilbert spaces and Hilbert C*-modules under the action of bounded operators is considered. It is shown that under some conditions, duals and approximate duals are stable under the action of bounded operators. Especially, the stability of duals and approximate duals under the morphisms of Hilbert C*-modules is studied.

کلیدواژه‌ها [English]

  • Hilbert space
  • Measure space
  • Hilbert C*-module
  • Frame
  • Bounded operator
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