International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Open Access | Fully Refereed | Peer Reviewed

ISSN: 2319-7064




Downloads: 83

Research Paper | Mathematics | India | Volume 9 Issue 10, October 2020


Contribution of the Duality Theory of ε - And Π -Tensor Products of Baire Spaces

Dr. Upendra Kumar Nirala


Abstract: The basic study of the tensor product of the duality theory is a locally convex space in terms of its dual is the central part of the modern theory of topological vector spaces, for it provides the setting for the deepest and most beautiful results of the subject. Various authors have mentioned In this paper we have proved that the dual space of the ε – tensor product of the two given metrizable locally convex spaces is equal to the ε – tensor product of their topological dual spaces. Duality theory of ε – tensor product of two metrizable locally convex spaces considered about topological dual space of tensor products. objective of this paper is For all our purposes, topological vector spaces are locally convex, in the sense of having a basis at consisting of convex opens. We prove below that a separating family of semi norms produces a locally convex topology. Conversely, every locally convex topology is given by separating families of semi-norms: the semi norms are functionals associated to a local basis of balanced, convex opens. Giving the topology on a locally convex V by a family of semi norms exhibits V as a dense subspace of a projective limit of Banach spaces, with the subspace topology. This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary


Keywords: tensor product, Metrizable, Locally, convex spaces, Topological dual spaces


Edition: Volume 9 Issue 10, October 2020,


Pages: 1408 - 1410


How to Cite this Article?

Dr. Upendra Kumar Nirala, "Contribution of the Duality Theory of ε - And Π -Tensor Products of Baire Spaces", International Journal of Science and Research (IJSR), https://www.ijsr.net/get_abstract.php?paper_id=SR201018115401, Volume 9 Issue 10, October 2020, 1408 - 1410

How to Share this Article?

Enter Your Email Address


Similar Articles with Keyword 'Locally'

Downloads: 144

M.Tech / M.E / PhD Thesis, Mathematics, India, Volume 6 Issue 8, August 2017

Pages: 1453 - 1457

Bianchi Type V String Having G and Λ as a Constant in a Cosmological Model

Versha Rani

Share this Article

Downloads: 102

Research Paper, Mathematics, India, Volume 4 Issue 1, January 2015

Pages: 1869 - 1874

Curvature Properties of Special (?, ?)- Finsler

Gayathri K, Narasimhamurthy.S.K

Share this Article

Similar Articles with Keyword 'tensor'

Downloads: 144

M.Tech / M.E / PhD Thesis, Mathematics, India, Volume 6 Issue 8, August 2017

Pages: 1453 - 1457

Bianchi Type V String Having G and Λ as a Constant in a Cosmological Model

Versha Rani

Share this Article

Downloads: 96

Research Paper, Mathematics, India, Volume 6 Issue 6, June 2017

Pages: 2800 - 2800

Theory of Quasi C-Reducible Finsler Manifold

T. S. Chauhan

Share this Article

Similar Articles with Keyword 'product'

Downloads: 1

Research Paper, Mathematics, Congo (DRC), Volume 10 Issue 5, May 2021

Pages: 571 - 577

Solvency and Reinsurance Treaty of an Automobile Portfolio: Case of Sub-Saharian Countries

Bukanga Maheshe Crispin, Mabela Makengo Matendo Rostin

Share this Article

Downloads: 2 | Weekly Hits: ⮙1 | Monthly Hits: ⮙1

Research Paper, Mathematics, India, Volume 10 Issue 11, November 2021

Pages: 103 - 105

On Certain Transformations of Poly-Basic Bilateral Hypergeometric Series

Dr. Brijesh Pratap Singh

Share this Article
Top