In this paper, we defi ne the notion of C-a ne maps in the unital -rings and we investigate the C -extreme points of the graph and epigraph of such maps. We show that for a C -convex map f defi ned on a unital -ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C -face of the epigraph of f. Moreover, we prove some results about the C  -faces of C -convex sets in -rings.

In this paper, we  nd explicit solution to the operator equation TXS 􀀀 SX T = A in the general setting of the adjointable operators between Hilbert C-modules, when T; S have closed ranges and S is a self adjoint operator.

Let A be an algebra. A linear mapping  : A! A is called a derivation if  (ab) =  (a)b + a (b) for each a; b 2 A. Given two derivations  and  0 on a C-algebra A, we prove that there exists a derivation
on A such that   0 =
2 if and only if either  0 = 0 or  = s 0 for some s 2 C.

We introduce variational inequality problems on Hilbert C-modules and we prove several existence results for variational inequalities de ned on closed convex sets. Then relation between variational inequalities, C-valued metric projection and  xed point theory on Hilbert C-modules is studied.

Let ,be a linear ,-endomorphism on a C ,-algebra A so that , (A) acts on a Hilbert space H which including K(H) and let f, tgt2R be a ,-C ,-dynamical system on A with the generator , : In this paper, we demonstrate some conditions under which f, tgt2R is implemented by a C0-groups of unitaries on H. In particular, we prove that for a rank-one projection p 2 A,which is invariant under , t,there is a C0-group futgt2R of unitaries in B(H) such that , t(a) = ut, (a)u ,t: Furthermore, introducing the concepts of ,-inner endomorphism and ,-bijective map, we prove that each ,-bijective linear endomorphism on A is a ,-inner endomorphism, where ,ia idempotent. Finally, as an application, we characterize each so-called ,-C ,-dynamical system on the concrete C ,-algebra A: = B(H) ,B(H),where H is a separable Hilbert space and ,is the linear ,-endomorphism , (S,T) = (0,T) on A:

The main purpose of this paper is to introduce the notion of -fusion frames in Hilbert modules over locally C-algebras to study some properties about these frames. We present some results of frames in the view of -fusion frames in Hilbert modules over locally C-algebras, inparticular we give the reconstruction formula for these frames.

Let A be a Banach algebra. We say that a sequence fDng1 n=0 of continuous operators form A into A is a local higher derivation if to each a 2 A there corresponds a continuous higher derivation fda; ng1 n=0 such that Dn(a) = da; n(a) for each non-negative integer n. We show that if A is a C-algebra then each local higher derivation on A is a higher derivation. We also prove that each local higher derivation on a C-algebra is automatically continuous.

The aim of this paper is to present a proof of the hyperbolicity of the family fc (x)=c (x-x3/3 ), |c|>3, on an its invariant subset of R.

In this paper, a new notion of frames is introduced: -operator frame as generalization of -frames in Hilbert C-modules introduced by A. Alijani and M. A. Dehghan [2] and we establish some results.