Abstract. In this paper, we introduce the concept of T−fuzzy interior ideal, T−fuzzy simple, T−fuzzy bi-ideal, and generalized T−fuzzy bi-ideal of a Γ−semigroup. We characterize Γ−semigroups through T−fuzzification. We find equivalent conditions on these fuzzy subsets in simple Γ−semigroups and Γ−semigroups. Finally, we establish a necessary and sufficient condition for a T -fuzzy bi-ideal to b...

We give conditions on a strongly continuous semigroup T and a bounded perturbation B such that the perturbed semigroup S preserves asymptotic properties as boundedness, asymptotic almost periodicity, uniform ergodicity and total uniform ergodicity. In the rst systematic treatise on perturbation of semigroups, R.S.Phillips 10] proved in 1953 that, if A is the innnitesimal generator of a strongly...

Let S be the model of a semigroup with an associate subgroup whose identity is a medial idempotent constructed by Blyth and Martins considered as a unary semigroup. For another such semigroup T , we construct all unary homomorphisms of S into T in terms of their parameters. On S we construct all unary congruences again directly from its parameters. This construction leads to a characterization ...

Given the infinitesimal generator A of a C0-semigroup on the Banach space X which satisfies the Kreiss resolvent condition, i.e., there exists an M > 0 such that ‖(sI−A)‖ ≤ M Re(s) for all complex s with positive real part. We show that for general Banach spaces this condition does not give any information on the growth of the associated C0-semigroup. For Hilbert spaces the situation is less dr...

It is known that a left C-wrpp semigroup can be described as curler structure of a left band and a C-wrpp semigroup. In this paper, we introduce the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass. We shall particularly show that the spined product of a left C-wrpp semigroup and a right normal band is a weakly left C-wrpp semifroup. ...

In this paper we describe the modulus semigroup of the C0-semigroup associated with the linear differential equation with delay { u1ptq Auptq Lut (t ¥ 0), up0q x∈X, u0 f ∈Lpp h, 0;Xq, in the Banach lattice X Lpp h, 0;Xq, where X is a Banach lattice with order continuous norm. The progress with respect to previous papers is that A may be an unbounded generator of a C0-semigroup possessing a modu...

We study the off-diagonal estimates for transition densities of diffusions and jump processes in a setting when they depend essentially only on the time and distance. We state and prove the dichotomy for the tail of the transition density. 1. Preliminaries Let (M, d) be a locally compact separable metric space and μ be a Radon measure on M with full support. Definition 1.1. A family {pt}t>0 of ...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...

In this note, we describe the generator of the modulus semigroup of the C0-semigroup associated with the delay equation { u′(t) = Au(t) + Lut, t > 0, u(0) = x ∈ R, u0 = f ∈ L(−h, 0;R) , in the Banach lattice R × L(−h, 0;R). MCS 2000: 34K06