In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

Moving human body detection is a significant research direction in the fields of image processing and computer vision. A new method of moving human body detection is proposed in this paper based on Kinect, which extracts depth images with Kinect, so that the moving object in which people are interested can be obtained without useless background information. Five consecutive frames of depth imag...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic operation, we have developed some aggregation operators for aggregating interval-valued dual hesitant fuzzy linguistic information: i...

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...

In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

We prove that two unital dual operator algebras A,B are stably isomorphic if and only if they are ∆-equivalent [7], if and only if they have completely isometric normal representations α, β on Hilbert spaces H,K respectively and there exists a ternary ring of operators M ⊂ B(H,K) such that α(A) = [M∗β(B)M]−w and β(B) = [Mα(A)M∗]−w .

where A and B are called the lower frame bound and upper frame bound, respectively. In particular, when A= B = 1, we say that {hk}k∈Z is a (normalized) tight frame in H. The 1 Research was partially supported by NSF Grants DMS-9872890, DMS-9706753 and AFOSR Grant F4962098-1-0044. Web: http://www.princeton.edu/~icd. 2 Research was supported by NSERC Canada under Grant G121210654 and by Alberta I...

We prove that two dual operator spaces X and Y are stably isomorphic if and only if there exist completely isometric normal representations φ and ψ of X and Y , respectively, and ternary rings of operators M1,M2 such that φ(X) = [M ∗ 2 ψ(Y )M1] −w ∗ and ψ(Y ) = [M2φ(X)M ∗ 1 ]. We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being ...