Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

For a connected reductive group $G$ defined over $\mathbb{F}_q$ and equipped with the induced Frobenius endomorphism $F$, we study relation among following three $\mathbb{Z}$-algebras: (i) $\mathbb{Z}$-model $\mathsf{E}_G$ of algebras Gelfand-Graev representations $G^F$; (ii) Grothendieck $\mathsf{K}_{G^\ast}$ category $G^{\ast F^\ast}$ $\overline{\mathbb{F}_q}$ (Deligne-Lusztig dual side); (ii...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

PURPOSE The goal of this study is to assess the interactions among alcohol consumption, cigarette smoking, and aspartate aminotransferase (AST) / alanine aminotransferase (ALT) ratios on esophageal cancer. MATERIALS AND METHODS Alcohol and the risk of incidence and death from esophageal cancer were examined in a 14-year prospective cohort study of 782,632 Korean men, 30 to 93 years of age, wh...