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Mal, Arpita

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Arpita Mal

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079-68261660

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Dr. Arpita Mal is an assistant professor at DA-IICT since December 2023. Prior to joining DA-IICT, she was an INSPIRE Faculty Fellow at IISc Bangalore. She completed her PhD from Jadavpur University in 2021. Her research interest is broadly in Functional Analysis, Operator Theory and Linear Algebra. In particular, it includes Geometry of Banach space, Birkohff-James orthogonality, Numerical radius etc.

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    Norm inequalities in L(X) and a geometric constant
    (Springer, 13-04-2024) Bhunia, Pintu; Mal, Arpita; Mal, Arpita; Mal, Arpita; Mal, Arpita; Mal, Arpita; Mal, Arpita; DA-IICT, Gandhinagar
    We introduce a new norm (say�?-norm) on�L(X),�the space of all bounded linear operators defined on a normed linear space�X. We explore various properties of the�?-norm. In addition, we study several equalities and inequalities of the�?-norm of operators on�X.�As an application, we obtain an upper bound for the numerical radius of product of operators, which improves a well-known upper bound of the numerical radius for sectorial matrices. We present the�?-norm of operators by using the extreme points of the unit ball of the corresponding spaces. Furthermore, we define a geometric constant (say�?-index) associated with�X�and study properties of the�?-index. In particular, we obtain the exact value of the�?-index for some polyhedral spaces and complex Hilbert space. Finally, we study the�?-index of�?p-sum of normed linear spaces.