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...

The 4 dimensional (4d) binomial matrix and its domains on the classical double sequence spaces $\mathcal{L}_{p}$, $\mathcal{M}_{u}$, $\mathcal{C}_{P}$, $\mathcal{C}_{bP}$, $\mathcal{C}_{r}$, $\mathcal{C}_{f}$ $\mathcal{C}_{f_0}$ have been described examined by Demiriz Erdem in papers \cite{e.d.2}-\cite{e.d.3}. In this article, we describe two with aid of aforementioned study some properties the...

Let $\mathcal{X}$ be a Banach space with fundamental biorthogonal system and let $\mathcal{Y}$ the dense subspace spanned by vectors of system. We prove that admits $C^\infty$-smooth norm locally depends on finitely many coordinates (LFC, for short), as well polyhedral coordinates. As consequence, we also finite, $\sigma$-uniformly discrete LFC partitions unity $C^1$-smooth LUR norm. This theor...

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

We study generalized special cycles on Hermitian locally symmetric spaces $$\Gamma \backslash D$$ associated to the groups $$G={{\mathrm {U}}}(p,q)$$ , $${{\mathrm {Sp}}}(2n,{\mathbb {R}}) $$ and {O}}}^*(2n) . These are algebraic covered by subgroups of G which same type. show that Poincaré duals these can be viewed as Fourier coefficients a theta series. This gives new cases lifts from cohomol...

We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1≤p≤∞, respectively, and prove that ℓpλ(B) and ℓ p are linearly isomorphic for 0<p≤∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1≤p<∞. Furthermore, we determine the alpha-, beta- and gamm...

The open-closed vertex in the maximally supersymmetric type IIB plane-wave light-cone string field theory is considered and an explicit solution for the bosonic part of the vertex is derived, valid for all values of the mass parameter, μ. This vertex is of relevance to IIB plane-wave orientifolds, as well as IIB plane-wave strings in the presence of D-branes and their gauge theory duals. Method...

We consider four weighted matching-type problems: the bipartite graph and general graph versions of matching and f -factors. The linear program duals for these problems are shown to be weights of certain subgraphs. Specifically the so-called y duals are the weights of certain maximum matchings or f -factors; z duals (used for general graphs) are the weights of certain 2-factors or 2f -factors. ...

In this paper, we introduce the sets of bounded, convergent and null series and the set of sequences of bounded variation of fuzzy numbers with the level sets. We investigate the relationships between these sets and their classical forms and give some properties including definitions, lemmas and various kind of fuzzy metric spaces. Furthermore, we study some of their properties like completenes...

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...