arXiv:2106.06790v1 [math.FA] 12 Jun 2021 Ideal of sequentially p-limited operators: a tensor product approach DEEPIKA BAWEJA, ALEENA PHILIP Department of Mathematics, BITS Pilani Hyderabad, 500078 deepika@hyderabad.bits-pilani.ac.in, p20190038@hyderabad.bits-pilani.ac.in Abstract In this article, we have studied some aspects of the operator ideal of se- quentially p-limited operators using the theory of tensor products. We have defined a tensor norm α p using the dual of the space of mid p-summing se- quences and proved that (X ˆ ⊗ αp Y ) ∗ is isometrically isomorphic to Lt p (X, Y ∗ ), the class of sequentially p-limited operators from X to Y ∗ . Finally using this tensor product representation, we find the dual of the operator ideal Lt p . Keywords : Sequentially p-limited operators, sequence classes, tensor norms, op- erator ideals, dual of an operator ideal. Mathematics Subject Classification : 46B28, 46B45 1 Introduction and Terminologies The class of sequentially p-limited operators has been introduced by Karn and Sinha [8] using the notion of operator p-summability. Since then, several authors have studied the ideal of sequentially p-limited operators in different contexts, see [1, 7, 12]. Moreover, several other operator ideals associated to the class of operator p-summable sequences have been defined and studied in [1, 3]. Most of these stud- ies involves only the theory of operator ideals. We believe that there is a lot more to explore about this operator ideal using the tensor product approach. Recently, Zeekoi[12] has proved that the class of sequentially p-limited operators is a maximal Banach operator ideal. Since there is a natural correspondence between maximal operator ideals and finitely generated tensor norms[5, Theorem 17.5], one can con- struct a tensor norm associated to the class of sequentially p-limited operators and 1