Abstract
In this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space l(1) of all absolutely summable sequences. Examples of nuclear operators over the space l(1) are given and used to construct operators over general Banach spaces with specific approximation numbers.