Results 11 to 20 of about 127 (112)
Distribution of genus numbers of abelian number fields
Journal of the London Mathematical Society, Volume 107, Issue 6, Page 2197-2217, June 2023., 2023 Abstract We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0%$0\%$ of the time.
Christopher Frei +2 more
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Complete form of Furuta inequality [PDF]
Proceedings of the American Mathematical Society, 2008 The authors give a Furuta type order preserving operator inequality (they call it \textit{complete form of the Furuta inequality}) as follows: Let \(A\) and \(B\) be bounded linear operators on a complex Hilbert space with \(A\geq B\geq 0\) and let \(r\geq 0\), \(p>p_{0}>0\) and \(s=\min\{p, 2p_{0}+\min\{1,r\}\}\).
Yuan, Jiangtao, Gao, Zongsheng
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Complements to the Furuta inequality
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fujii, Masatoshi +2 more
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Around the Furuta inequality the operator inequalities [PDF]
International Journal of Mathematics and Mathematical Sciences, 1993 For positive operators A and B with A invertible it is shown that implies . The inequalities in the title for 0 ≤ B ≤ A are then derived as a conquence.
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Further extension of Furuta inequality [PDF]
Journal of Mathematical Inequalities, 2010 If A2n A2n−1 ··· A2 A1 B 0, with A1 > 0,t1,t2,···,tn−1, tn ∈ (0,1) and p1,p2,···,p2n−1,p2n 1 for a natural number n. Then the following inequality holds for r tn A2n 1−t n+r {A2n r 2 (A2n−1 −tn 2 {A2(n−1) tn−1 2 ···A4 t2 2 (A3 −t2 2 {A2 t1 2 (A1 −t1 2 B p1A1 −t1 2 ) p2 A2 t1 2 } p3A3 −t2 2 ) p4A4 t2 2 ···A2(n−1) tn−1 2 } p2n−1A2n−1 ...
Changsen Yang, Yaqing Wang
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The best possibility of the grand Furuta inequality [PDF]
Proceedings of the American Mathematical Society, 1999 Let A , B ∈
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On a reverse Heinz–Kato–Furuta inequality
Linear Algebra and its Applications, 2012 In a Minkowski inner product space \((M, [\cdot,\cdot]_J)\), for timelike \(x\) and arbitary \(y\), we have the reverse Schwarz inequality: \[ |[x,y]_J|^2\geq [x,x]_J [y,y]_J. \] In this paper, the authors generalize it to several types of inequalities. The first two are Theorem 3.1 (reverse determinant Hadamard theorem).
Bebiano, N. +2 more
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Some Properties of Furuta Type Inequalities and Applications [PDF]
Abstract and Applied Analysis, 2014 This work is to consider Furuta type inequalities and their applications. Firstly, some Furuta type inequalities underA≥B≥0are obtained via Loewner-Heinz inequality; as an application, a proof of Furuta inequality is given without using the invertibility of operators.
Jiangtao Yuan, Caihong Wang
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Best possibility of the Furuta inequality [PDF]
Proceedings of the American Mathematical Society, 1996 Let 0 ≤ p ,
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Grand Furuta inequality and its variant [PDF]
Journal of Mathematical Inequalities, 2007 The grand Furuta inequality (GFI) is understood as follows: If positive operators A and B on a Hilbert space satisfy A B 0,A is invertible and t ∈ (0,1) ,t hen A 1−t+r (A r (A − t B p A − t ) s A r ) 1 t+r (pt)s+r holds for p, s 1a ndr t . In this note, we present a short proof of (GFI) which is done by the usual induction on s and the use of the ...
Masatoshi Fujii +2 more
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