Sain, Debmalya and Ray, Anubhab and Paul, Kallol
(2019)
*Extreme Contractions on Finite-Dimensional Polygonal Banach Spaces.*
In: JOURNAL OF CONVEX ANALYSIS, 26
(3).
pp. 877-885.

## Abstract

We explore extreme contractions on finite-dimensional polygonal Banach spaces, from the point of view of attainment of norm of a linear operator. We prove that if X is an n-dimensional polygonal Banach space and Y is any normed linear space and T is an element of L(X, Y) is an extreme contraction, then T attains norm at n linearly independent extreme points of B-X. Moreover, if T attains norm at n linearly independent extreme points x(1), x(2), ..., x(n), of B-X and does not attain norm at any other extreme point of B-X, then each T-x(i), is an extreme point of B-Y. We completely characterize extreme contractions between a finite-dimensional polygonal Banach space and a strictly convex normed linear space. We introduce L-P property for a pair of Banach spaces and show that it has natural connections with our present study. We also prove that for any strictly convex Banach space X and any finite-dimensional polygonal Banach space Y, the pair (X, Y) does not have L-P property. Finally, we obtain a characterization of Hilbert spaces among strictly convex Banach spaces in terms of L-P property.

Item Type: | Journal Article |
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Publication: | JOURNAL OF CONVEX ANALYSIS |

Publisher: | HELDERMANN VERLAG |

Additional Information: | copyright for this article belongs to HELDERMANN VERLAG |

Keywords: | Extreme contractions; polygonal Banach spaces; strict convexity; Hilbert spaces |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 29 Nov 2019 10:26 |

Last Modified: | 29 Nov 2019 10:26 |

URI: | http://eprints.iisc.ac.in/id/eprint/64023 |

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