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A note on isometries of Lipschitz spaces
, Article Journal of Mathematical Analysis and Applications ; Vol. 411, Issue. 2 , 2014 , Pages 555-558 ; ISSN: 0022247X ; Sharif University of Technology
Abstract
The main purpose of this article is to generalize a recent result about isometries of Lipschitz spaces. Botelho, Fleming and Jamison [2] described surjective linear isometries between vector-valued Lipschitz spaces under certain conditions. In this article, we extend the main result of [2] by removing the quasi-sub-reflexivity condition from Banach spaces
A Correlation Measure Based on Vector-Valued Lp -Norms
, Article IEEE Transactions on Information Theory ; Volume 65, Issue 12 , 2019 , Pages 7985-8004 ; 00189448 (ISSN) ; Beigi, S ; Gohari, A ; Yassaee, M. H ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
In this paper, we introduce a new measure of correlation for bipartite quantum states. This measure depends on a parameter α , and is defined in terms of vector-valued Lp -norms. The measure is within a constant of the exponential of α -Rényi mutual information, and reduces to the trace norm (total variation distance) for α =1. We will prove some decoupling type theorems in terms of this measure of correlation, and present some applications in privacy amplification as well as in bounding the random coding exponents. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the α -Rényi mutual information according to...
An Analytical Approach to Monge’s Problem
, M.Sc. Thesis Sharif University of Technology ; Ranjbar Motlagh, Alireza (Supervisor)
Abstract
Monge’s problem was solved by Brenier in 1990. In general, the problem remained unresolved for a long time. some of its cases were solved by assumptions, but the general case and its analytical solution for the first time by Ian Bernier The French mathematician was introduced. He wrote his famous article Solved this nonlinear problem with technical assumptions. With the help of convex analysis and fundamental theorems in functions with vector values, he proved the existence and unity of this nonlinear problem. Monge’s problem, also known as optimal transport, suggests whether a stablesized mapping can be done by having two probabilistic spaces and one cost function. (Inverted image of any...
A correlation measure based on vector-valued Lp norms
, Article 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 July 2019 through 12 July 2019 ; Volume 2019-July , 2019 , Pages 1132-1136 ; 21578095 (ISSN); 9781538692912 (ISBN) ; Beigi, S ; Gohari, A ; Yassaee, M. H ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
In this paper, a new measure of correlation is introduced. This measure depends on a parameter α, and is defined in terms of vector-valued Lp norms. The measure is within a constant of the exponential of α-Rényi mutual information, and reduces to the trace norm (total variation distance) for α = 1. We provide some properties and applications of this measure of correlation. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the α-Rényi mutual information according to Csiszár's proposal. © 2019 IEEE