A generalized arithmetic-geometric mean-type inequality of measurable operator

2022 ◽  
pp. 1-13
Author(s):  
Shuoxi Sun ◽  
Cheng Yan
Keyword(s):  
Geometric Mean ◽  
Type Inequality ◽  
Measurable Operator ◽  
Generalized Arithmetic

scholarly journals GALOIS THEORY OF THE CANONICAL THETA STRUCTURE

2011 ◽  
Vol 07 (01) ◽  
pp. 173-202
Author(s):  
ROBERT CARLS
Keyword(s):  
Galois Theory ◽  
Theoretical Foundation ◽  
Abelian Varieties ◽  
Geometric Mean ◽  
Null Point ◽  
Point Counting ◽  
Characteristic 2 ◽  
Theoretic Characterization ◽  
Generalized Arithmetic

In this article, we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application, we prove some 2-adic theta identities which describe the set of canonical theta null points of the canonical lifts of ordinary abelian varieties in characteristic 2. The latter theta relations are suitable for explicit canonical lifting. Using the theory of canonical theta null points, we are able to give a theoretical foundation to Mestre's point counting algorithm which is based on the computation of the generalized arithmetic geometric mean sequence.

scholarly journals ARITHMETIC-GEOMETRIC MEANS FOR HYPERELLIPTIC CURVES AND CALABI–YAU VARIETIES

2010 ◽  
Vol 21 (07) ◽  
pp. 939-949 ◽  
Author(s):  
KEIJI MATSUMOTO ◽  
TOMOHIDE TERASOMA
Keyword(s):  
Projective Space ◽  
Hyperelliptic Curve ◽  
Geometric Mean ◽  
Hyperelliptic Curves ◽  
Double Cover ◽  
The Other ◽  
Geometric Means ◽  
Dimensional Projective Space ◽  
Period Integral ◽  
Generalized Arithmetic

In this paper, we define a generalized arithmetic-geometric mean μg among 2g terms motivated by 2τ-formulas of theta constants. By using Thomae's formula, we give two expressions of μg when initial terms satisfy some conditions. One is given in terms of period integrals of a hyperelliptic curve C of genus g. The other is by a period integral of a certain Calabi–Yau g-fold given as a double cover of the g-dimensional projective space Pg.

A Generalized Arithmetic-Geometric Mean

SIAM Review ◽  
1983 ◽  
Vol 25 (3) ◽  
pp. 401-401 ◽  
Author(s):  
D. Borwein ◽  
P. B. Borwein
Keyword(s):  
Geometric Mean ◽  
Generalized Arithmetic

A Generalized Arithmetic-Geometric Mean

SIAM Review ◽  
1984 ◽  
Vol 26 (3) ◽  
pp. 433-433
Author(s):  
D. Borwein
Keyword(s):  
Geometric Mean ◽  
Generalized Arithmetic

scholarly journals Buzano inequality in inner product C*-modules via the operator geometric mean

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1689-1694
Author(s):  
Jun Fujii ◽  
Masatoshi Fujii ◽  
Yuki Seo
Keyword(s):  
Geometric Mean ◽  
Type Inequality ◽  
Schwarz Inequality ◽  
Inner Product

In this paper, by means of the operator geometric mean, we show a Buzano type inequality in an inner product C*-module, which is an extension of the Cauchy-Schwarz inequality in an inner product C*-module.

scholarly journals Symmetric Polynomials and Symmetric Mean Inequalities

10.37236/2915 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Karl Mahlburg ◽  
Clifford Smyth
Keyword(s):  
Geometric Mean ◽  
Symmetric Polynomials ◽  
Homogeneous Polynomials ◽  
Combinatorial Result ◽  
A Cell ◽  
Generalized Arithmetic

We prove generalized arithmetic-geometric mean inequalities for quasi-means arising from symmetric polynomials. The inequalities are satisfied by all positive, homogeneous symmetric polynomials, as well as a certain family of non-homogeneous polynomials; this family allows us to prove the following combinatorial result for marked square grids.Suppose that the cells of a $n \times n$ checkerboard are each independently filled or empty, where the probability that a cell is filled depends only on its column. We prove that for any $0 \leq \ell \leq n$, the probability that each column has at most $\ell$ filled sites is less than or equal to the probability that each row has at most $\ell$ filled sites.

scholarly journals Further generalizations of some operator inequalities involving positive linear map

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2355-2364 ◽  
Author(s):  
Changsen Yang ◽  
Chaojun Yang
Keyword(s):  
Geometric Mean ◽  
Type Inequality ◽  
Operator Inequality ◽  
Power Mean ◽  
Positive Real ◽  
Operator Inequalities ◽  
Linear Map ◽  
Linear Maps ◽  
Positive Linear Map ◽  
Karcher Mean

We obtain a generalized conclusion based on an ?-geometric mean inequality. The conclusion is presented as follows: If m1,M1,m2,M2 are positive real numbers, 0 < m1 ? A ? M1 and 0 < m2 ? B ? M2 for m1 < M1 and m2 < M2, then for every unital positive linear map ? and ? ? (0,1], the operator inequality below holds: (?(?)#??(B))p ? 1/16 {(M1+m1)2((M1+m1)-1(M2+m2))2?)/(m2M2)?(m1M1)1- ?}p ?p(A#?B), p ? 2. Likewise, we give a second powering of the Diaz-Metcalf type inequality. Finally, we present p-th powering of some reversed inequalities for n operators related to Karcher mean and power mean involving positive linear maps.

scholarly journals Hyperelliptic integrals and generalized arithmetic–geometric mean

2012 ◽  
Vol 28 (1) ◽  
pp. 61-78 ◽  
Author(s):  
Jeroen Spandaw ◽  
Duco van Straten
Keyword(s):  
Geometric Mean ◽  
Generalized Arithmetic
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