scholarly journals Estimates of (1+x)1/x involved in Carleman’s inequality and Keller’s limit

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1535-1539 ◽  
Author(s):  
Cristinel Mortici ◽  
X.J. Jang
Keyword(s):  
Simple Proof ◽  
Direct Proof ◽  
Constant E ◽  
Carleman’S Inequality ◽  
Keller’S Limit ◽  
Carleman's Inequality

The aim of this work is to extend the results obtained by Yang Bicheng and L. Debnath in [Some inequalities involving the constant e and an application to Carleman?s inequality, J. Math. Anal. Appl., 223 (1998), 347-353]. We present a simple proof of our new result which can be also used as a direct proof for Yang Bicheng and L. Debnath results. Finally some applications to generalized Keller?s limit and further directions are provided.

scholarly journals On some convergences to the constant e and improvements of Carleman’s inequality

2015 ◽  
Vol 31 (2) ◽  
pp. 249-254
Author(s):  
CRISTINEL MORTICI ◽  
◽  
HU YUE ◽  
Keyword(s):  
Constant E ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

We present sharp inequalities related to the sequence (1 + 1/n)n and some applications to Kellers’ limit and Carleman’s inequality.

On strengthened weighted Carleman's inequality

2003 ◽  
Vol 68 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Aleksandra Čižmešija ◽  
Josip Pecarić ◽  
Lars–Erik Persson
Keyword(s):  
Geometric Mean ◽  
Weighted Arithmetic ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.

Carleman's Inequality

2003 ◽  
Vol 110 (5) ◽  
pp. 424-431 ◽  
Author(s):  
John Duncan ◽  
Colin M. McGregor
Keyword(s):  
Carleman’S Inequality ◽  
Carleman's Inequality

A simple proof of the Mazur-Orlicz summability theorem

1981 ◽  
Vol 89 (3) ◽  
pp. 391-392 ◽  
Author(s):  
J. A. Fridy
Keyword(s):  
Functional Analysis ◽  
Simple Proof ◽  
Direct Proof ◽  
Topological Properties ◽  
Unbounded Sequence ◽  
Important Theorem ◽  
Slowly Oscillating Sequences

In 1933(1), Mazur and Orlicz stated that, if a conservative (i.e. convergence preserving) matrix sums a bounded nonconvergent sequence, then it must sum an unbounded sequence. Their proof of this result (2) was one of the early applications of functional analysis to summability theory, and it is based on rather deep topological properties of F K-spaces. In (3) Zeller obtained a proof of this important theorem as a consequence of his study of the summability of slowly oscillating sequences. The purpose of this note is to give a simple direct proof of this theorem using only the well-known Silverman-Töplitz conditions for regularity. In order to reduce the details of the argument, we state and prove the result for regular matrices rather than conservative matrices.

scholarly journals A Simple Proof of the Jamiołkowski Criterion for Complete Positivity of Linear Maps

2005 ◽  
Vol 12 (01) ◽  
pp. 55-64 ◽  
Author(s):  
D. Salgado ◽  
J. L. Sánchez-Gómez ◽  
M. Ferrero
Keyword(s):  
Simple Proof ◽  
Direct Proof ◽  
Complete Positivity ◽  
Systematic Method ◽  
Completely Positive ◽  
Linear Map ◽  
Matrix Algebras ◽  
Linear Maps ◽  
Kraus Decomposition

We give a simple direct proof of the Jamiołkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accessible for physicists than other ones found in the literature and provides a systematic method to give any set of Kraus matrices of the Kraus decomposition.

Sign in / Sign up

Export Citation Format

Share Document