Let T (t), 0 ≤ t < ∞, be a one parameter c0-semigroup of bounded linear operators on a Banach space X with infinitesimal generator A and R(λ, A) be the resolvent operator of A. The Hille-Yosida Theorem for c0-semigroups asserts that the resolvent operator of the infinitesimal generator A satisfies ‖R(λ, A)‖ ≤ M λ−ω for some constants M > 0 and λ ∈ R (the set of real numbers), λ > ω. The object ...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior combine amplitude damping, inverse and pure dephasing. show mixing channels can result in restoring unitality, whereas commutative lead to non-commutativity. For Markovian semigroups, prove classical uncertainties cannot break quantum Markovianity. Moreover, contrary Pauli c...

in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck&apos;s functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

Let T(X) be the full transformation semigroup on a nonempty set X. For ? Z Y X, let T(X,Y,Z) = {? T(X):Y? Z}. It is not difficult to see that it generalized form of three well-known semigroups. This paper obtains an isomorphism theorem T(X,Y,Z). In addition, when X finite and rank calculated.

For every Banach space (Y, ‖ · ‖Y ) that admits an equivalent uniformly convex norm we prove that there exists c = c(Y ) ∈ (0,∞) with the following property. Suppose that n ∈ N and that X is an n-dimensional normed space with unit ball BX . Then for every 1-Lipschitz function f : BX → Y and for every ε ∈ (0, 1/2] there exists a radius r > exp(−1/ε), a point x ∈ BX with x + rBX ⊆ BX , and an aff...

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...

A member of a class of evolution systems is defined by averaBing a oneparameter family of invertible transformations G with a semigroup T The resulting evolution system, U(t,s) G(t)T(t-s)G(s) -1, preserves continuity and strong continuity, and in case G is a linear family, may have an identifiable generator and resolvent both of which are constructed from T. Occurrences of the class of evolutio...

By using a special t-level relation U(μ, t) = {(x, y) ∈ S × S|(μ(x) ∧ μ(y)) ∨ IdS(x, y) ≥ t} based on a fuzzy ideal μ of a semigroup S, which is a congruence relation, we study the roughness of soft semigroups under this special ideal of S, such as rough soft subsemigroups, rough soft ideals and rough soft prime ideals.