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11,603 results on '"Rao, T."'

11. Geometry of the unit ball of ${\mathcal L}(X,Y^*)$

Author

Rao, T. S. S. R. K. and Seal, Susmita

Subjects
Mathematics - Functional Analysis, 46A22, 46B10, 46B25, 46B20, 46B22
Abstract

In this paper we study the geometry of the unit ball of the space of operators ${\mathcal L}(X,Y^*)$, by considering the projective tensor product $X\hat{\otimes}_{\pi} Y$ as a predual. We prove that if an elementary tensor (rank one operator) of the form $x_0^*\otimes y_0^* $ in the unit sphere $ S_{{\mathcal L}(X,Y^*)}$ is a $w^*$-strongly extreme point of unit ball, then $x_0^*$ is $w^*$-strongly extreme point of unit ball of $X^*$ and $y_0^*$ is $w^*$-strongly extreme point of the unit ball of $Y^*$. We show that similar conclusion holds if the rank one operator is a point of weak$^*$-weak continuity for the identity mapping on the unit sphere of ${\mathcal L}(X,Y^*)$. We also study extremal phenomenon in the unit ball of ${\mathcal L}(X,Y^*)^*$. We show that if a point $z\in S_{{\mathcal L}(X,Y^*)^*}$ is a $w^*$-strongly extreme point of the unit ball, then $z=x\otimes y$ for some $w^*$-strongly extreme points $x\in S_X$ and $y\in S_Y$, provided the space of compact operators, $\mathcal{K}(X,Y^*)$ is separating for $X\hat{\otimes}_{\pi} Y$.

Published
2025

15. MEOP based 3He polarization and injection system for experiments below 1 K

Author

Rao, T., Barron-Palos, L., Berkutov, I., Crawford, C., Golub, R., Huffman, P., Konieczny, M., Korobkina, E., Reid, Austin, Salazar-Angeles, B., Smith, C., and Tat, R.

Subjects
Physics - Instrumentation and Detectors
Abstract

Metastability exchange optical pumping (MEOP) is a widely used technique for producing polarized $^{3}$He. In connection with an experiment to search for the electric dipole moment of the neutron (nEDM) we have built a MEOP based $^{3}$He polarization and injection system to prepare 80 % polarized $^{3}$He at room temperature which will be injected into a ~400 mK measurement cell filled with superfluid $^{4}$He. We describe the polarization and injection system, which is designed to allow for final concentrations of $10^{-8}-10^{-10}$ of 80 % polarized $^{3}$He in the superfluid filled measurement cell. Only $\approx0.72\%$ polarization loss due to gradients is expected during injection

Published
2024

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