共查询到20条相似文献,搜索用时 31 毫秒
1.
Takayuki Furuta 《Proceedings of the American Mathematical Society》1996,124(10):3071-3075
We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.
2.
Chia Shiang Lin 《数学学报(英文版)》2001,17(4):657-668
In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance)
inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove
uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and
equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be
expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.
Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000 相似文献
3.
杨长森 《数学物理学报(B辑英文版)》2008,28(4):998-1002
Furuta showed that if A≥B≥0,then for each r≥0,f(p)=(A^r/2 B^p A^r/2)^t+r/p+r is decreasing for p≥t≥0.Using this result,the following inequality(C^r/2(AB^2A)^δC^ r/2)^ p-1+r/4δ+r ≤C^p-1+r is obtained for 0〈p ≤1,r≥1,1/4≤δ≤1 and three positive operators A, B, C satisfy(A^1/2BA^1/2)^p/2≤A^p,(B^1/2AB^1/2)^p/2≥B^p,(C^1/2AC^1/2)^p/2≤C^p,(A^1/2CA^1/2)^p/2≥A^p. 相似文献
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6.
Masatoshi Fujii Eizaburo Kamei 《Proceedings of the American Mathematical Society》1996,124(9):2751-2756
Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If and is invertible, then for each ,
is a decreasing function of both and for all and . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.
7.
In a recent paper, Domokos and Kolumbán introduced variational inequalities with operator solutions to provide a suitable
unified approach to several kinds of variational inequality and vector variational inequality in Banach spaces. Inspired by
their work, in this paper, we further develop the new scheme of vector variational inequalities with operator solutions from
the single-valued case into the multi-valued one. We prove the existence of solutions of generalized vector variational inequalities
with operator solutions and generalized quasi-vector variational inequalities with operator solutions. Some applications to
generalized vector variational inequalities and generalized quasi-vector variational inequalities in a normed space are also
provided. 相似文献
8.
Peng Gao 《Proceedings of the American Mathematical Society》2005,133(7):1977-1984
We use a theorem of Cartlidge and the technique of Redheffer's ``recurrent inequalities" to give some results on inequalities related to Hardy's inequality.
9.
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
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11.
Masatoshi Fujii Ritsuo Nakamoto 《Proceedings of the American Mathematical Society》2000,128(1):223-228
We give an extension of Lin's recent improvement of a generalized Schwarz inequality, which is based on the Heinz-Kato-Furuta inequality. As a consequence, we can sharpen the Heinz-Kato-Furuta inequality.
12.
Rodrigo Bañ uelos Rafal Latala Pedro J. Mé ndez-Herná ndez 《Proceedings of the American Mathematical Society》2001,129(10):2997-3008
We derive an inequality for multiple integrals from which we conclude various generalized isoperimetric inequalities for Brownian motion and symmetric stable processes in convex domains of fixed inradius. Our multiple integral inequality is a replacement for the classical inequality of H. J. Brascamp, E. H. Lieb and J. M. Luttinger, where instead of fixing the volume of the domain one fixes its inradius.
13.
The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional p-Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi?–Adamovi?’s inequality, Lazarevi?’s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa–Huygens-type inequalities, are generalized to the case of generalized functions. 相似文献
14.
Fuad Kittaneh 《Proceedings of the American Mathematical Society》2006,134(2):385-390
We prove several spectral radius inequalities for sums, products, and commutators of Hilbert space operators. Pinching inequalities for the spectral radius are also obtained.
15.
Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of ?eby?ev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized. 相似文献
16.
Rasul A. Khan 《Journal of Theoretical Probability》2009,22(2):348-364
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
相似文献
17.
In this paper,we study some functional inequalities(such as Poincaré inequality,logarithmic Sobolev inequality,generalized Cheeger isoperimetric inequality,transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of(random) path method.We provide estimates of the involved constants. 相似文献
18.
向量似变分不等式解的存在性及解集的稳定性 总被引:3,自引:0,他引:3
本文首先得到一类广义向量似变分不等式问题的解的存在性定理,然后利用usco映射的性质,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数(在Baire分类意义下)广义向量似变分不等式问题的解集是稳定的;另外还引入广义向量似变分不等式解集的本质连通区的概念,并证明了满足一定连续性、凸性条件的广义向量似变分不等式的解集至少存在一个本质连通区. 相似文献
19.
建立了复正定矩阵的几个行列式不等式,将正定Hermite阵的Minkowski不等式、 Ostrowski-Taussky不等式推广到了复正定矩阵上,推广改进了一些文献的结果. 相似文献
20.
We prove some sharp Hardy inequality associated with the gradient ? ?? = (? x ,|x| ?? ? y ) by a direct and simple approach. Moreover, similar method is applied to obtain some weighted sharp Rellich inequality related to the Grushin operator in the setting of L p . We also get some weighted Hardy and Rellich type inequalities related to a class of Greiner type operators. 相似文献