Results 31 to 40 of about 13,431 (178)

Catalytic majorization and $\ell_p$ norms [PDF]

, 2007
An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local ...
Aubrun, Guillaume, Nechita, Ion
core   +2 more sources

Submultiplicativity vs subadditivity for unitarily invariant norms

Linear Algebra and its Applications, 2004
The authors prove that if \(A\) and \(B\) are two \(n\)-by-\(n\) nonzero positive semidefinite matrices and \(\|\cdot\|\) is a unitarily invariant norm on matrices satisfying \(\|\text{diag}(1,0,\dots, 0)\|\geq 1\), then the inequalities \[ {\| AB\|\over\| A\|\,\| B\|}\leq {\| A+ B\|\over\| A\|+\| B\|}\quad\text{and}\quad {\| A\circ B\|\over \| A\|\,\|
Hiai, Fumio, Zhan, Xingzhi
openaire   +2 more sources

Unitarily invariant norm inequalities for operators

Journal of the Egyptian Mathematical Society, 2012
10 pages, Accepted ...
Erfanian Omidvar, M., Moslehian, M.S., Niknam, A.   +2 more
openaire   +2 more sources

Operator Monotone Functions and Convexity of Its Derivatives Norms

پژوهش‌های ریاضی, 2021
Introduction  Given the important role convex and quasi-convex functions play in many areas of mathematics and especially in optimization, one of the inequalities that has attracted the attention of many mathematicians in recent decades is Hermit ...
Zahra Rahimi Chegeni, amir ghasem ghazanfari, Kamal Falahi   +2 more
doaj  

Volume ratio, sparsity, and minimaxity under unitarily invariant norms [PDF]

2013 IEEE International Symposium on Information Theory, 2013
The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the convex geometry of finite-dimensional Banach spaces, we first develop a volume ratio approach for determining minimax ...
Ma, Zongming, Wu, Yihong
openaire   +3 more sources

Operator theory and function theory in Drury-Arveson space and its quotients [PDF]

, 2014
The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module.
A Arias, A Arias, A Athavale, A Athavale, A Beurling, A Volberg, AE Frazho, BVR Bhat, C Ambrozie, C Ambrozie, D Alpay, D Alpay, D Alpay, D Sarason, DC Greene, DW Kribs, E Tchoundja, F-H Vasilescu, G Popescu, G Popescu, G Popescu, G Popescu, G Popescu, G Popescu, GM Henkin, J Agler, J Agler, J Arazy, J Eschmeier, J Eschmeier, J Gleason, J Neumann von, JA Ball, JA Ball, JA Ball, JA Ball, JA Ball, JA Ball, JM Ortega, JW Bunce, K Guo, K Guo, KC Lin, KR Davidson, KR Davidson, KR Davidson, KR Davidson, KR Davidson, KR Davidson, L Carleson, L Carleson, M Andersson, M Hartz, M Kennedy, M Kerr, N Arcozzi, NTh Varopoulos, NTh Varopoulos, OM Shalit, OM Shalit, P Quiggin, PD Lax, PR Halmos, PS Muhly, PS Muhly, PS Muhly, Q Fang, Q Fang, RG Douglas, RG Douglas, RG Douglas, S Costea, S McCullough, S McCullough, S Richter, S Treil, SG Krantz, SW Drury, T Andô, TT Trent, V Bolotnikov, V Müller, W Rudin, WB Arveson, WB Arveson, WB Arveson, WB Arveson, WB Arveson, WB Arveson, WB Arveson, WB Arveson, WF Stinespring, X Fang, Z Chen   +93 more
core   +1 more source

Norm inequalities related to the Heron and Heinz means [PDF]

, 2017
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference version of the ...
Conde, C., Kapil, Y., Moslehian, M. S., Sababheh, M., Singh, M.   +4 more
core   +2 more sources

A note on the $C$-numerical radius and the $\lambda$-Aluthge transform in finite factors

, 2017
We prove that for any two elements $A$, $B$ in a factor $M$, if $B$ commutes with all the unitary conjugates of $A$, then either $A$ or $B$ is in $\mathbb{C}I$.
Fang, Junsheng, Wen, Shilin, Zhou, Xiaoyan   +2 more
core   +1 more source

Maps on classes of Hilbert space operators preserving measure of commutativity [PDF]

, 2014
In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily invariant norm ...
Gehér, György Pál, Nagy, Gergő
core   +2 more sources

UNITARILY INVARIANT NORMS ON FINITE VON NEUMANN ALGEBRAS [PDF]

, 2018
John von Neumann’s 1937 characterization of unitarily invariant norms on the n × n matrices in terms of symmetric gauge norms on Cn had a huge impact on linear algebra. In 2008 his results were extended to Ifactor von Neumann algebras by J.
Fan, Haihui
core   +1 more source