EQUATIONS
Print ISSN: 2944-9146, E-ISSN: 2732-9976 An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering
Volume 2, 2022
Trace Class in Separable Reflexive Banach Spaces, Lidskii Theorem
Author:
Abstract: In this article, we generalize definitions of the trace class operators for the reflexive Banach spaces and develop the Lidskii theory for Hilbert spaces to incorporate a larger class of reflexive Banach spaces for which the analog of trace class operators can be introduced. The approximation for the compact operator $$A\in B_{c}(X,Y)$$ on reflexive Banach spaces by the set of finite rank operators $$B_{Ran}(X,Y)$$ is proposed and its properties are established.