Abstract
For 1 ≤ p < ∞, it is known that the set K^*_p contains of all Lambert multipliers acting between L^p-spaces is a Banach space. In this study, we introduce a new induced norm by conditional expectation operators to show that K^*_p is a commutative Banach algebra with respect to this norm. Furthermore, in main result, the Fredholm *-multiplication operators on L^p-spaces are characterized, and some more results are obtained.
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