The Role of Sufism in Spreading Islam and Fighting Atonement

This paper delivered the need for Islamic thought to confront the Takfiri thought, through the return of Sufi thought. Sufism does not have fatwa to kill others, Sufism talks about tolerance, the love of the Prophet, and the non-compulsion of others tojoin either Islam or the way the murid belongs to. Sufism represents the spiritual and faithful state of Islam, the core of Islam. This paper find out the role of Sufism in the spread of Islam; in the past, and the contemporary in the fight against atonement. The aim of this paper is to describe the culture of Sufism, this paper studies the intellectual of Sufism, Sufim cultural, and politics as well. This paper studied about three main axis of Sufism; the culture and history of Sufism, the role of Sufism in spreading Islam, and the role of Sufism in addressing the Takfiri thought. Based on this study, the Islamic institution and government should adopt and adapt the Sufi thought, and to address the Takfiri culture, to prevent Muslim from joining the Takfiri groups

Sphere and projective space of a C*-algebra with a faithful state

Let 𝒜 be a unital C*-algebra with a faithful state ϕ. We study the geometry of the unit sphere 𝕊ϕ = {x ∈ 𝒜 : ϕ(x*x) = 1} and the projective space ℙϕ = 𝕊ϕ/𝕋. These spaces are shown to be smooth manifolds and homogeneous spaces of the group 𝒰ϕ(𝒜) of isomorphisms acting in 𝒜 which preserve the inner product induced by ϕ, which is a smooth Banach-Lie group. An important role is played by the theory of operators in Banach spaces with two norms, as developed by M.G. Krein and P. Lax. We define a metric in ℙϕ, and prove the existence of minimal geodesics, both with given initial data, and given endpoints.

STRICT COHERENCE ON MANY-VALUED EVENTS

We investigate the property of strict coherence in the setting of many-valued logics. Our main results read as follows: (i) a map from an MV-algebra to [0,1] is strictly coherent if and only if it satisfies Carnap’s regularity condition, and (ii) a [0,1]-valued book on a finite set of many-valued events is strictly coherent if and only if it extends to a faithful state of an MV-algebra that contains them. Remarkably this latter result allows us to relax the rather demanding conditions for the Shimony-Kemeny characterisation of strict coherence put forward in the mid 1950s in this Journal.

TWISTED COMMUTING SQUARES

We consider generalizations of commuting squares, called twisted commuting squares, obtained by having the commuting square orthogonality condition hold with respect to the inner product given by a faithful state on a finite-dimensional *-algebra. We present various examples of twisted commuting squares, most of which are computationally easy to work with, and we prove an isolation result. We also show how parametric families of (not necessarily) twisted commuting squares yield associative deformations of the matrix multiplication.

ON QUANTUM SEMIGROUP ACTIONS ON FINITE QUANTUM SPACES

We show that a continuous action of a quantum semigroup [Formula: see text] on a finite quantum space (finite dimensional C*-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification [Formula: see text] of [Formula: see text]. Using the classification of continuous compact quantum group actions on M2, we give a complete description of all continuous quantum semigroup actions on this quantum space preserving a faithful state.

Invariant states and ergodic dynamical systems on W*-algebras

An amenable semigroup of positive linear unital mappings on a W*-algebra is considered. Two main questions are dealt with: the existence of a normal faithful state invariant with respect to this semigroup and the description of ergodicity conditions. An explicit form of the ergodic projection, useful in treating the ergodicity problems, is also derived.