In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space...

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

We show that the symbol of a bounded composition operator on Wiener algebra Dirichlet series does not need to belong this algebra. Our example even gives an absolutely summing (hence compact) operator.

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...