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Rajendra Bhatia

Bio: Rajendra Bhatia is an academic researcher from University of Toronto. The author has contributed to research in topics: Eigenvalues and eigenvectors & Normal matrix. The author has an hindex of 2, co-authored 2 publications receiving 13 citations.

Papers
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01 Jan 1999
TL;DR: In this article, the bounds for perturbation of eigenvalues of normal matrices are shown to remain true for compact perturbations of normal operators, if extended eigenvalue sets are considered in the sense introduced by T. Kato.
Abstract: Various bounds for perturbation of eigenvalues of normal matrices are shown to remain true for compact perturbations of normal operators, if “extended” eigenvalue sets are considered in the sense introduced by T. Kato.

10 citations


Cited by
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Journal ArticleDOI
TL;DR: In matrix theory, majorization plays a significant role as discussed by the authors, and majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities.

137 citations

Book ChapterDOI
TL;DR: In this article, the distribution of eigenvalues of closed linear operators which are not selfadjoint is studied, with a focus on those operators that are obtained as perturbations of self-adjoint linear operators.
Abstract: The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are explained and elaborated. One approach uses complex analysis to study a holomorphic function whose zeros can be identified with the eigenvalues of the linear operator. The second method is an operator theoretic approach involvingthe numerical range. General results obtained by the two methods are derived and compared. Applications to non-selfadjoint Jacobi and Schrodinger operators are considered. Some possible directions for future research are discussed.

83 citations

Journal ArticleDOI
TL;DR: For bounded linear operators A, B on a Hilbert space, this paper showed that the Schatten-p-norm of B − A is bounded from above by the sum over all discrete eigenvalues of B and Num(A) denotes the numerical range of A. They applied this estimate to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrodinger operators.
Abstract: For bounded linear operators A, B on a Hilbert space $${\mathcal{H}}$$ we show that $${ \sum_{\lambda}{\rm dist}(\lambda, {\rm Num}(A))^p}$$ is bounded from above by the Schatten-p-norm of B − A. Here, the sum is taken over all discrete eigenvalues of B and Num(A) denotes the numerical range of A. We apply this estimate to recover and improve some Lieb–Thirring type inequalities for non-selfadjoint Jacobi and Schrodinger operators.

61 citations

Journal ArticleDOI
TL;DR: For bounded linear operators, this article showed the validity of the Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrodinger operators on a Hilbert space.
Abstract: For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{ um}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrodinger operators.

34 citations