In this paper we investigate the semigroup structure of the syntactic monoid Syn(C+) of C+, the semigroup generated by a maximal prefix code C for which C+ is a single class of the syntactic congruence. In particular we prove that for such a prefix code C, either Syn(C+) is a group or it is isomorphic to a special type of submonoid of G× T (R) where G is a group and T (R) is the full transforma...

We consider flows (X,T), given by actions (t,x)→tx, on a compact metric space X with discrete T as an acting group. study new class of - the Strongly Rigid (SR) flows, that are properly contained in distal (D) and contain all equicontinuous (EQ) flows. Thus, EQflows⫋SRflows⫋Dflows. The concepts equicontinuity, strong rigidity distality coincide for induced flow (2X,T). observe strongly rigid (X...

We extend some classical results of Cowling and Meda to the noncommutative setting. Let (Tt)t>0 be a symmetric contraction semigroup on a noncommutative space Lp(M), and let the functions φ and ψ be regularly related. We prove that the semigroup (Tt)t>0 is φ-ultracontractive, i.e. ‖Ttx‖∞ ≤ Cφ(t)‖x‖1 for all x ∈ L1(M) and t > 0 if and only if its infinitesimal generator L has the Sobolev embeddi...

It is known that every semigroup of normal completely positive maps P = {Pt : t ≥ 0} of B(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0-semigroup acting on B(K) for some Hilbert space K ⊇ H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the ind...

real spectrum (ARS)finitely closed subset of, 52morphism of, 31projective limits of, 31residue space of, 66–69saturated subset of, 56subspace of, 61algebraLukasiewicz, 84Kleene, 87Post, 84AOSclosed subset, 210dependent subset, 210AOS-fan, 166archimedean-equivalent, 188ARS-fan, 170connected components, 208finiteisomorphi...

We know that if S is a subsemigroup of a semitopological semigroup T , and stands for one of the spaces , , , or , and ( ,T ) denotes the canonical -compactification of T , where T has the property that (S) = (T)|s , then ( |s , (S)) is an -compactification of S. In this paper, we try to show the converse of this problem when T is a locally compact group and S is a closed normal subgroup of T ....

We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary nitely generated inverse subsemigroup of S and T. We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows th...

The setting of this research is Bishop’s constructive mathematics. Let q be an anticongruence on a semigroup S with apartness. For q we say that it is an rectangular band anticongruence if S/q is a rectangular band. In paper [12] a construction of the maximal rectangular band anticongruence on a semigroup is described. This paper is continuation of that research. Let T be a detachable subsemigr...

We give simple bounds for the exponential decay of a strongly continuous semigroup V (t) = exp(At) in a Hilbert space. The bounds are expressed by means of the solution X of the Ljapunov equation A X + XA = ?I and the quantity sup 0th kV (t)k for small h. Our main bound is attained on any normal semigroup and can therefore not be improved in general. Let V (t) be a strongly continuous semigroup...

For a quantum Markov semigroup T on the algebra B(h) with a faithful invariant state ρ, we can define an adjoint T̃ with respect to the scalar product determined by ρ. In this paper, we solve the open problems of characterising adjoints T̃ that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators H,Lk in the Gorini Kossakowski Sudarshan Lindblad...