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Let A be a complex, commutative, and semisimple Banach algebra and let T be a power bounded multiplier on A. We prove a Katznelson-Tzafriri type theorem for T. As an application, we give some results concerning convergence of the sequence {T(n)a} (a is an element of A). Some related problems are also discussed.

Let G be a locally compact abelian group with the dual group Γ, M (G), the measure algebra of G, and Mr (G), the largest regular subalgebra of M (G). For a power bounded measure µ ∈ M (G), we put Fµ = {γ ∈ Γ : µb (γ) = 1} and Eµ = {γ ∈ Γ : |µb (γ)| = 1} , where µb is the Fourier-Stieltjes transform of µ. Let (Ω, Σ, m) be a σ−finite positive measure space and let Θ = {θg}g∈G be an action of G in (Ω, Σ, m) by invertible measure preserving transformations. Any action Θ induces a representation T = {Tg}g∈G of G on L p (Ω) (1 ≤ p < ∞) by invertible isometries, where (Tgf) (ω) = f (θgω). If Θ is continuous, then for any µ ∈ M (G), we can define a bounded linear operator on L p (Ω) (1 ≤ p < ∞) associated with µ, denoted by Tµ, which integrates Tg with respect to µ. Theorem. Let µ ∈ Mr (G) be power bounded and 1 < p < ∞. If Fµ = Eµ, then the sequence { Tn µ f } converges strongly for every f ∈ L p (G).

On behalf of the Organizing Committee, we are very pleased to welcome you to the 3nd International Confer- ence of Mathematical Sciences (ICMS 2019) to be held between 4-8 September 2019 at Maltepe University in Istanbul. We hope that, ICMS 2019 will be one of the most beneficial scientific events, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in any field of science.

Let T = {T(t)}(t >= 0) be a continuous semigroup of contractions on a Hilbert space. We define A(T) as the closure of the set {(f) over cap (T) : f is an element of L-1 (R+)} with respect to the operator-norm topology, where (f) over cap (T) =

Let T = {T(t)}(t >= 0) be a bounded Co-semigroup on a Banach space with generator A. We define A(T) as the closure with respect to the operator-norm topology of the set {f(T): f epsilon L-1(R+)}, where f (T) = integral(infinity)(0) f(t)T(t) dt is the Laplace transform of f epsilon L-1 (R+) with respect to the semigroup T. Then A(T) is a commutative Banach algebra. It is shown that if the unitary spectrurn sigma(A)boolean AND iR of A is at most countable, then the Gelfand transform of S epsilon A(T) vanishes on sigma(A)boolean AND iR if and only if, lim(t ->infinity) parallel to T(t)S parallel to = 0. Some applications to the semisimplicity problem are given.