TL;DR
This paper investigates the properties of first EP modular operators on Hilbert C*-modules and establishes conditions under which their products are also EP, extending existing results to broader algebraic contexts.
Contribution
It provides necessary and sufficient conditions for the product of two EP modular operators to be EP, generalizing previous work to arbitrary C*-algebras and compact operator C*-algebras.
Findings
Characterization of EP modular operators on Hilbert C*-modules
Necessary and sufficient conditions for product of EP operators to be EP
Extension of Koliha's results to broader C*-algebra classes
Abstract
We study first EP modular operators on Hilbert C*-modules and then we provide necessary and sufficient conditions for the product of two EP modular operators to be EP. These enable us to extend some results of Koliha [{\it Studia Math.} {\bf 139} (2000), 81--90.] for an arbitrary C*-algebra and the C*-algebras of compact operators.
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