The study on controlled g-frames and controlled fusion frames in Hilbert C*-modules

Subject Areas : Statistics

M. Rashidi-Kouchi ¹

1 - Young Researchers and Elite Club Kahnooj Branch, Islamic Azad University, Kahnooj, Iran.

Received: 2018-04-09 Accepted : 2019-05-01 Published : 2019-11-01

Keywords: *C-مدول هیلبرتی٬ قاب٬ g-قاب٬ قاب تلفیقی٬ قاب کنترل شده,

Abstract :

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than in the field of complex numbers.In this paper, we define and characterize controlled g-frames and controlled fusion frames in Hilbert C*-modules. These are generalization of controlled frames in Hilbert C*-modules and also controlled g-frames and controlled fusion frames in Hilbert spaces. We show, similar in Hilbert space, every controlled g-frame in Hilbert C*-module is an usual g-frame. Also we study the relation between controlled fusion frames and fusion frames in Hilbert C*-modules. Finally we present a sufficient condition on a family of closed submodules to be a controlled fusion frame.

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