TAILIEUCHUNG - Some properties of C-fusion frames

In this article we give some important properties about the generalization, namely erasures of subspaces, the bound of c-erasure reconstruction error for Parseval c-fusion frames, perturbation of c-fusion frames and the frame operator for fusion pair. | Turk J Math 34 (2010) , 393 – 415. ¨ ITAK ˙ c TUB doi: Some properties of C -fusion frames Mohammad Hasan Faroughi and Reza Ahmadi Abstract In [10], we generalized the concept of fusion frames, namely, c -fusion frames, which is a continuous version of the fusion frames. In this article we give some important properties about the generalization, namely erasures of subspaces, the bound of c -erasure reconstruction error for Parseval c -fusion frames, perturbation of c -fusion frames and the frame operator for fusion pair. Key Words: Operator, Hilbert space, Bessel, Frame, Fusion frame, c -fusion frame 1. Introduction and preliminaries Throughout this paper H will be a Hilbert space and H will be the collection of all closed subspace of H . Also, (X, μ) will be a measure space, and v : X → [0, +∞) a measurable mapping such that v = 0 almost everywhere (.). We shall denote the unit closed ball of H by H1 . Frames was first introduced in the context of non-harmonic Fourier series [9]. Outside of signal processing, frames did not seem to generate much interest until the ground breaking work in [8]. Since then the theory of frames began to be more widely studied. During the last 20 years the theory of frames has grown up rapidly, with the development of several new applications. For example, besides traditional application as signal processing, image processing, data compression, and sampling theory, frames are now used to mitigate the effect of losses in pocket-based communication systems and hence to improve the robustness of data transmission on [6], and to design high-rate constellation with full diversity in multiple-antenna code design [12]. In [2, 1, 3] some applications have been developed. The fusion frames were considered by Casazza, Kutyniok and Li in connection with distributed processing and are related to the construction of global frames [4, 5]. The fusion frame theory is in fact more delicate due to complicated relations .