Advances in Difference Equations (Dec 2019)
Operators constructed by means of basic sequences and nuclear matrices
Abstract
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 ℓ1 $\ell _{1}$ of all absolutely summable sequences. Examples of nuclear operators over the space ℓ1 $\ell _{1}$ are given and used to construct operators over general Banach spaces with specific approximation numbers.
Keywords