منابع مشابه
Extensions of Heinz - Kato - Furuta
Reprints available directly from the publisher Photocopying permitted by license only (C) 1999 OPA (Overseas Publishers Association) N.V. In our preceding note, we discussed a generalized Schwarz inequality, an improvement of the Heinz-Kato-Furuta inequality and an inequality related to the Furuta inequality. In succession, we give further discussions on them from the viewpoint of the covarianc...
متن کاملComplete Form of Furuta Inequality
Let A and B be bounded linear operators on a Hilbert space satisfying A ≥ B ≥ 0. The well-known Furuta inequality is given as follows: Let r ≥ 0 and p > 0; then A r 2 Amin{1,p}A r 2 ≥ (A r 2 BpA r 2 ) min{1,p}+r p+r . In order to give a self-contained proof of it, Furuta (1989) proved that if 1 ≥ r ≥ 0, p > p0 > 0 and 2p0 + r ≥ p > p0, then (A r 2 Bp0A r 2 ) p+r p0+r ≥ (A r 2 BpA r 2 ) p+r p+r ...
متن کاملThe Kato-ponce Inequality
In this article we revisit the inequalities of Kato and Ponce concerning the L norm of the Bessel potential J = (1 − ∆) (or Riesz potential D = (−∆)) of the product of two functions in terms of the product of the L norm of one function and the L norm of the the Bessel potential J (resp. Riesz potential D) of the other function. Here the indices p, q, and r are related as in Hölder’s inequality ...
متن کاملSome new extensions of Hardy`s inequality
In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions
متن کاملFuruta Inequality and Its Related Topics
This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Löwner-Heinz inequality to Furuta inequality, 2. Ando–Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order. 1. From Löwner-Heinz inequality to Furuta inequality. The noncommutativity of operators appears in the fact that t is not orderpreserving. That is, there ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05242-9