Abstract
We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.
Highlights
Frame for a Hilbert space was first introduced by Duffin and Schaeffer [4] in 1952 to study some fundamental problems in non-harmonic Fourier series
A generalized fusion frame is used to generalize the theory of fusion frame and g-frame
Frame operator for the pair of g-fusion Bessel sequences was studied by the authors in [8], who presented the stability of dual g-fusion frames in Hilbert spaces in [7]
Summary
Frame for a Hilbert space was first introduced by Duffin and Schaeffer [4] in 1952 to study some fundamental problems in non-harmonic Fourier series. The relation between the frame operators for the pair of controlled g-fusion Bessel sequences in Hilbert spaces and the tensor product of Hilbert spaces is obtained.
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