共查询到20条相似文献,搜索用时 46 毫秒
1.
Summary A recent note by Marshall and Olkin (1990), in which the Cauchy-Schwarz and Kantorovich inequalities are considered in matrix versions expressed in terms of the Loewner partial ordering, is extended to cover positive semidefinite matrices in addition to positive definite ones.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth 相似文献
2.
Eric Schippers 《Journal d'Analyse Mathématique》2006,98(1):249-277
The coefficients of a quadratic differential which is changing under the Loewner flow satisfy a well-known differential system
studied by Schiffer, Schaeffer and Spencer, and others. By work of Roth, this differential system can be interpreted as Hamilton's
equations. We apply the power matrix to interpret this differential system in terms of the coadjoint action of the matrix
group on the dual of its Lie algebra. As an application, we derive a set of integral invariants of Hamilton's equations which
is in a certain sense complete. In function theoretic terms, these are expressions in the coefficients of the quadratic differential
and Loewner map which are independent of the parameter in the Loewner flow. 相似文献
3.
A generalized matrix version of reverse Cauchy-Schwarz/Hölder inequality is proved. This includes the recent results proved by Bourin, Fujii, Lee, Niezgoda and Seo. 相似文献
4.
The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality. 相似文献
5.
We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreîn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions areJ-self-adjoint.Research supported in part by the Romanian Academy grant GAR-6645/1996.This research was supported in part by NSF grant DMS-9501223. 相似文献
6.
Full ordering in the Shorrocks mobility sense of the semiring of monotone doubly stochastic matrices
In this paper, we investigate the ordering on a semiring of monotone doubly stochastic transition matrices in Shorrocks’ sense. We identify a class of an equilibrium index of mobility that induces the full ordering in a semiring, while this ordering is compatible with Dardanoni’s partial ordering on a set of monotone primitive irreducible doubly stochastic matrices. 相似文献
7.
J.M. Fernandez-Ponce 《Journal of multivariate analysis》2003,85(1):40-53
A multivariate dispersion ordering based on quantiles more widely separated is defined. This new multivariate dispersion ordering is a generalization of the classic univariate version. If we vary the ordering of the components in the multivariate random variable then the comparison could not be possible. We provide a characterization using a multivariate expansion function. The relationship among various multivariate orderings is also considered. Finally, several examples illustrate the method of this paper. 相似文献
8.
We give a matrix version of the scalar inequality f(a + b) ? f(a) + f(b) for positive concave functions f on [0, ∞). We show that Choi’s inequality for positive unital maps and operator convex functions remains valid for monotone convex functions at the cost of unitary congruences. Some inequalities for log-convex functions are presented and a new arithmetic-geometric mean inequality for positive matrices is given. We also point out a simple proof of the Bhatia-Kittaneh arithmetic-geometric mean inequality. 相似文献
9.
Guillermo Ayala 《Journal of multivariate analysis》2009,100(7):1447-1464
A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a Rd-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Different analyses are included using an image database of human corneal endothelia. 相似文献
10.
In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs. 相似文献
11.
In this paper,a new version of the general form of the main inequality of Reich-Strebel is given.As applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense. 相似文献
12.
本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示. 相似文献
13.
A matrix trace inequality and its application 总被引:1,自引:0,他引:1
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson inequality for positive semidefinite matrices. 相似文献
14.
This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequality relating the row and column sums of 0-1 matrices in the course of his work on number theory. As pointed out by van Dam [6], Khinchin’s inequality can be viewed as a generalization of the classical Cauchy inequality. Van Dam went on to derive analogs of Khinchin’s inequality for arbitrary matrices. We carry this work forward, first by proving even more than general matrix results, and then by formulating them in a way that allows us to apply limiting arguments to create new integral inequalities for functions of two variables. These integral inequalities can be interpreted as giving information about conditional expectations. 相似文献
15.
The problem under consideration is a maximization problem over a constraint set defined by a finite number of inequality and equality constraints over an arbitrary set in a reflexive Banach space. A generalization of the Kuhn-Tucker necessary conditions is developed where neither the objective function nor the constraint functions are required to be differentiable. A new constraint qualification is imposed in order to validate the optimality criteria. It is shown that this qualification is the weakest possible in the sense that it is necessary for the optimality criteria to hold at the point under investigation for all families of objective functions having a constrained local maximum at this point 相似文献
16.
Dušan R. Georgijević 《Integral Equations and Operator Theory》2002,42(2):183-200
A solvability condition for matrix valued directional single-node interpolation problems of Loewner type is established, in terms of properties of Pick kernel. As a consequence, a solvability condition for matrix valued directional truncated Hamburger moment problems is obtained. 相似文献
17.
The Loewner partial ordering between nonnegative definite matrices M and B1MB is considered. The main result obtained generalizes a number of results known in the literature. The rank subtractivity partial ordering and the Drazin partial ordering between M and B1MB are also discussed. 相似文献
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19.
Jagjit Singh Matharu Mohammad Sal Moslehian Jaspal Singh Aujla 《Linear algebra and its applications》2011,435(2):270-276
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr’s inequality due to Vasi? and Ke?ki?. 相似文献
20.
In this note we present a new proof and an extension of the Hilbert space operators version of an inequality by Bohr. 相似文献