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1
Content available remote

Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality

100%
Koizumi T., Watanabe K.
Open Mathematics
|
2013
|
tom 11
|
nr 2
368-375
EN
We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.
2
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Inequalities Of Lipschitz Type For Power Series In Banach Algebras

81%
Dragomir S. S.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
61-83
EN
Let [...] f(z)=∑n=0∞αnzn $f(z) = \sum\nolimits_{n = 0}^\infty {\alpha _n z^n }$ be a function defined by power series with complex coefficients and convergent on the open disk D (0, R) ⊂ ℂ, R > 0. For any x, y ∈ ℬ, a Banach algebra, with ‖x‖, ‖y‖ < R we show among others that [...] ‖f(y)−f(x)‖≤‖y−x‖∫01fa′(‖(1−t)x+ty‖)dt $$\left\| {f(y) - f(x)} \right\| \le \left\| {y - x} \right\|\int_0^1 {f_a^\prime } (\left\| {(1 - t)x + ty} \right\|)dt$$ where [...] fa(z)=∑n=0∞|αn| zn $f_a (z) = \sum\nolimits_{n = 0}^\infty {|\alpha _n |} \;z^n$ . Inequalities for the commutator such as [...] ‖f(x)f(y)−f(y)f(x)‖≤2fa(M)fa′(M)‖y−x‖, $$\left\| {f(x)f(y) - f(y)f(x)} \right\| \le 2f_a (M)f_a^\prime (M)\left\| {y - x} \right\|,$$ if ‖x‖, ‖y‖ ≤ M < R, as well as some inequalities of Hermite–Hadamard type are also provided.
3
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Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

81%
Dragomir S. S.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
39-62
EN
Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.
4
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Operator inequalities of Jensen type

61%
Moslehian M. S., Mićić J., Kian M.
Topological Algebra and its Applications
|
2013
|
tom 1
9-21
EN
We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]
5
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Improved Heinz inequalities via the Jensen functional

52%
Krnić M., Pečarić J.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1698-1710
EN
By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.
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