Quotients of bounded linear operators on non-Archimedean Banach spaces

Abstract

Let $X$ be a non-Archimedean Banach space over $\mathbb{K}$ and let $A,B\in B(X).$ In this paper, we define the quotient of bounded linear operators $A$ and $B$ on non-Archimedean Banach space with $N(A)\subseteq N(B)$ as the mapping $Ax\mapsto Bx,$ for all $x\in X.$ We show some results about it. Majorization, range inclusion and factorization are studied, open mapping theorem for quotients of bounded linear operators is investigated and examples are given on non-Archimedean Banach spaces.