AMNM PROPERTY ON VARIATION SEQUENCE SPACES

In this paper, we will show that the spaces of p-bounded variation sequences are AMNM. AMS Subject Classification: 47B37, 47A25


Introduction
We write ω for the set of all complex sequences x = (x k ) ∞ k=0 .Let φ, l ∞ and c 0 denote the set of all finite, bounded and null sequences.We write l p = {x ∈ ω : The set bv p also arise from the sets l p , that is a sequence x is in bv p , if and only if the sequence (x k − x k−1 ) ∞ k=0 is in l p .It is this concept rather than the first one plays an important role in our studies.
url: www.acadpubl.eu§ Correspondence author a linear metric space X is called Schuader basis if, for every x ∈ X there is a unique sequence (λ n ) of scalars such that x = ∞ n=0 λ n b (n) .An F K space is a complete linear metric sequence space with the property that convergence implies coordinatewise convergence.A BK space is a normed F K space.An F K space X containing φ is said to have AK if every sequence , that is x = lim n→∞ x [n] .If A is a Banach algebra, then the set of all linear functionals on A is denoted by A * and the set of all its nonzero multiplicative functionals is denoted by Â.
. Also, we say that A is an algebra in which approximately multiplicative functionals are near multiplicative functionals, or A is AM N M for short, if for each ε > 0 there is δ > 0 such that d(ϕ) < ε whenever ϕ is a δ−multiplicative linear functional.
B. E. Johnson has shown that various Banach algebras are AM N M and some of them fail to be AM N M ( [1]).Also, this property is still unknown for some Banach algebras such as H ∞ and Douglas algebras.In this paper we will show that bv p is AM N M.For this topics on this sources see [1][2][3][4].

Main Results
In this section we investigate bv p as a Banach algebra that is AM N M .It has been proved that bv p is a Banach space with BK property.
(iii) The space bv p is a commutative Banach algebra.