Faculty Publications

Publications by NITK Faculty

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Factorization of EP Operators in Krein Spaces
(Springer, 2021) Vinoth, A.; Johnson, P.
A closed range bounded operator on a Hilbert space is said to be an EP operator if the operator commutes with its Moore-Penrose inverse. In this paper, we characterize EP operators through factorization in the Krein space settings. Â© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
Riesz Bases in Krein Spaces
(Indian National Science Academy, 2025) Jahan, S.; Johnson, P.
We start by introducing and studying the definition of a Riesz basis in a Krein space (K,[.,.]), along with a condition under which a Riesz basis becomes a Bessel sequence. The concept of biorthogonal sequence in Krein spaces is also introduced, providing an equivalent characterization of a Riesz basis. Additionally, we explore the concept of the Gram matrix, defined as the sum of a positive and a negative Gram matrices, and specify conditions under which the Gram matrix becomes bounded in Krein spaces. Further, we characterize the conditions under which the Gram matrices {[fn,fj]n,j?I+} and {[fn,fj]n,j?I-} become bounded invertible operators. Finally, we provide an equivalent characterization of a Riesz basis in terms of Gram matrices. © The Indian National Science Academy 2025.