for an evolution family (U(t, s))t≤s≤0 on X . We refer to [5, 12] where these equations have been introduced and to [10, 13] for concrete examples. In particular, we showed in [12] that (1.1) and the abstract Cauchy problem associated to an operator ( ,D( )) on the product space := X × L(R−,X) are “equivalent.” Since, under appropriate conditions, the operator ( ,D( )) is the generator of a str...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

Let H be a separable Hilbert space. Given two strongly commuting CP0-semigroups φ and θ on B(H), there is a Hilbert space K ⊇ H and two (strongly) commuting E0-semigroups α and β such that φs ◦ θt(PHAPH) = PHαs ◦ βt(A)PH for all s, t ≥ 0 and all A ∈ B(K). In this note we prove that if φ is not an automorphism semigroup then α is cocycle conjugate to the minimal ∗-endomorphic dilation of φ, and ...

Let iX, T) be a transformation group with compact Hausdorff phase space X. The points x and y of A" are said to be proximal provided, whenever ß is a member of the unique compatible uniformity of X, there exists i£ T such that (x/, yt) GßIf x and y are not proximal, they are said to be distal. Let P denote the proximal relation in X. P is a reflexive, symmetric, T invariant relation, but is not...

Let K be a nonempty subset of a Hilbert space , where K is not necessarily closed and convex. A family Γ= {T(t); t ≥ 0} of mappings T(t) is called a semigroup on K if (S1) T(t) is a mapping from K into itself for t ≥ 0, (S2) T(0)x = x and T(t+ s)x = T(t)T(s)x for x ∈ K and t,s≥ 0, (S3) for each x ∈ K , T(·)x is strongly measurable and bounded on every bounded subinterval of [0,∞). Let Γ be a se...

Let {T (t)} t≥0 be a C-semigroup on a Banach space X with generator A. We will investigate the asymptotic almost periodicity of {T (t)} via the Hille-Yosida space of its generator.

Let {T (t) : t > 0} be a strongly continuous semigroup of linear contractions in Lp, 1 < p < ∞, of a σ-finite measure space. In this paper we prove that if there corresponds to each t > 0 a positive linear contraction P (t) in Lp such that |T (t)f | ≤ P (t)|f | for all f ∈ Lp, then there exists a strongly continuous semigroup {S(t) : t > 0} of positive linear contractions in Lp such that |T (t)...

1. In a recent paper [4], Sevrin has given necessary and sufficient conditions for a subsemigroup of the free product of a free group and a free semigroup to be of the same form; in particular he deduces that a subsemigroup T oí a free semigroup 5 is free if and only if1 1. For any aET, sES, if as ET and saET, then sET. Now whereas the property of being a free subsemigroup of S is absolute, i.e...

We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem u′(t) + Au(t) = f(t, u(t), Tu(t)), t ∈ J, t 6= tk, ∆u|t=tk = Ik(u(tk)), k = 1, 2, . . . , m, u(0) = x0, where A : D(A) ⊂ E → E is a closed linear operator and −A generates a strongly continuous semigroup T (t)(t ≥ 0) in E. Under ...

In this paper we present a decoding principle for BCH, Alternant and Goppa codes constructed through a semigroup ring, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r, i.e., whose minimum Hamming distance is 2r + 1. Key-word: Semigroup rings, BCH codes, Alternant codes, Goppa codes, modified BerlekampMassey algorithm.