مجله موجکها و جبر خطی
سال هفتم شماره 1 (Spring and Summer 2020)

In this paper, we study the excess of continuous K-g-frames and give some results about this notion. Also, we extend the concept of atomic system to continuous version and study its relations by continuous K-g-frames. Indeed, we give some equivalent characterizations for continuous K-g-frames. As well as, the relationship of a continuous K-g-frame and the range of operator K will be verified. Finally, we study the induced cK-frames by continuous K-g-frames.

Trace and some other interesting properties of Haar wavelets matrix of size $ 2^K$ are studied by Shiralashetti and Kumbinarasaiah [6], results related to the trace of Haar wavelets matrix derived based on K is even or odd and the same is concluded in Theorem 3:2. This article deals with the trace of Haar wavelets matrix in depth by identifying and overcoming the pitfalls occur in the proof of Theorem 3.2.

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In this paper, we intend to introduce the concept of weaving continuous g-frames in separable Hilbert spaces. Then, we present some new results on these frames and also we show that it is enough to check continuous g-woven in smaller measurable space than the original space. We investigate the relationship between these frames and c-woven frames. Sufficient conditions will also be given for these frames. Finally, we verify the perturbation of weaving continuous g-frames.

‎Consider a locally compact group $G$ with two compact subgroups $H$ and $K$‎. ‎Equip the double coset space $Ksetminus G/H$ with the quotient topology‎. ‎Suppose that $mu$ is an $N$-relatively invariant measure‎, ‎on $Ksetminus G/H$‎. ‎We define a multiplication on $L^1(Ksetminus G/H,mu)$ such that this space becomes a Banach algebra that possesses a left (right) approximate identity‎.
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In this paper, we reintroduce the concept of controlled K-frames and then, we show that this definition is equivalent with the concept that has been recently introduced in cite{Nouri}. Meanwhile, we correct one of the results which were obtained in the mentioned paper. In the sequel, we construct some new controlled K-frames by some operator theory tools. Finally, we provide some conditions under which the sum of two controlled K-frames remains a controlled K-frame.

It is well known that if a real valued convex function on a compact convex domain contained in the real numbers attains its maximum, then it does so at least at one extreme point of its domain. In this paper, we consider a matrix convex function on a compact and $C^*$-convex set generated by self--adjoint matrices. An important issue is so that this function on a compact and $C^*$-convex domain attains its maximum at a $C^*$-extreme point.
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