in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family version of the result, and used it to determine the structure of deformation rings over characteristic zero fields. As a corollary, we obtain the L-invariant ...

Single side band modulation is a widespread technique in communication with significant impact on communication technologies such as DSL modems and ATSC TV. Its widespread utilization is due to its bandwidth and power saving characteristics. In this paper, we present a new scheme for SSB signal generation which is cost efficient and enjoys superior characteristics in terms of frequency stabilit...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

When describing a quantum mechanical system, it is convenient to consider state vectors that do not belong to the Hilbert space. In the rst part of this paper, we survey the various formalisms have been introduced for giving a rigorous mathematical justiication to this procedure: rigged Hilbert spaces (RHS), scales or lattices of Hilbert spaces (LHS), nested Hilbert spaces, partial inner produc...

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...