Let \(E\) be an \(o\)-complete Banach lattice, \(X\) a complex vector space and \(p\) from \(X\) into \(E\) a Kantorovich norm. The triple \((X,p,E)\) is called a lattice normed space. A lattice normed space is said to be \(br\)-complete if for any sequence \((x_n)\) in \(X\) from \(p(x_n-x_m) \xrightarrow{r} 0\) the existence of \(x\in X\) such that \(p(x_n-x) \xrightarrow{r} 0\) follows. The author considers a lattice normed space \(X\) and majorizable and \(r\)-compact operators defined on \(X\). Then he shows the following result: Theorem 1.3. Let \((X,p,E)\) be a \(br\)-complete linear normed space and let \(E'\) and \(E\) be Banach lattices with an order continuous norm. Each \(r\)-compact majorizable operator \(T\) from \(X\) into \(X\) has an \(r\)-compact exact majorant, i.e. a smallest operator majorizing \(T\). Then considering the spectrum \(\sigma(T)\) of a majorizable operator \(T\) as an operator and the spectrum \(\sigma_0(T)\) of \(T\) as a majorizable operator he shows Theorem 2.2. For any \(r\)-compact and majorizable operator \(T\) from \(X\) into \(X\) we have \(\sigma(T)=\sigma_0(T)\). At the end of the paper he shows that summing operators as well as regular operators between special lattice normed spaces are majorizable and he also gives sufficient conditions for the equality \(\sigma(T)=\sigma_0(T)\) to be true.