in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

Between the laminar epidermis and the laminar dermis of laminar region (LR) in equine foot, it can be observed the basement membrane zone (BMZ), which is composed of a basement membrane and its accompaniments like the hemidesmosome and anchoring fibril. Alteration in the BMZ in equine laminitis is possibly related with not only development but also recovery outcome and recurrence of this diseas...

and the re ported angiographic in ci dence was 0.044%. Sin gle cor o nary ar tery with anom a lous or i gin of the right cor o nary ar tery (RCA) from the left main (LM) stem is even rarer and was once thought to be a be nign con di tion. As the anom a lous RCA orig i nates from the LM stem, it can pass an te rior to the pul mo nary trunk, pos te rior to the aor tic root, or be tween these two ...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.