Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
Some lower bounds for the numerical radius of Hilbert space operators
98
107
EN
Ali
Zamani
zamani.ali85@yahoo.com
10.22034/aot.1612-1076
We show that if $T$ is a bounded linear operator on a complex Hilbert space, then<br />begin{equation*}<br />frac{1}{2}Vert TVertleq sqrt{frac{w^2(T)}{2} + frac{w(T)}{2}sqrt{w^2(T) - c^2(T)}} leq w(T),<br />end{equation*}<br />where $w(cdot)$ and $c(cdot)$ are the numerical radius and the Crawford number, respectively.<br />We then apply it to prove that for each $tin[0, frac{1}{2})$ and natural number $k$,<br />begin{equation*}<br />frac{(1 + 2t)^{frac{1}{2k}}}{{2}^{frac{1}{k}}}m(T)leq w(T),<br />end{equation*}<br />where $m(T)$ denotes the minimum modulus of $T$. Some other related results are also presented.
Numerical radius,operator norm,inequality,Cartesian decomposition
http://www.aot-math.org/article_42504.html
http://www.aot-math.org/article_42504_e092353b73c1ef28452661188909e86f.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
On maps compressing the numerical range between $C^*$-algebras
108
113
EN
Aschwag Fahad
Albideewi
msmabrouk@uqu.edu.sa
Mohamed
Mabruk
FSG Tunisia
mbs_mabrouk@yahoo.fr
10.22034/aot.1612-1067
In this paper, we deal with the problem of characterizing linear maps compressing the numerical range. A<br />counterexample is given to show that such a map need not be a Jordan *-homomorphism in general even if the C*-algebras are commutative. Next, under an auxiliary condition we show that such a map is a Jordan *-homomorphism.
Numerical Range,C*-algebra, compressing the numerical range, Jordan *-homomorphism
http://www.aot-math.org/article_43297.html
http://www.aot-math.org/article_43297_6b4eade500bac4d1f7c5e7db5bb95166.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
Normalized tight vs. general frames in sampling problems
114
125
EN
Tomaž
Košir
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
tomaz.kosir@fmf.uni-lj.si
Matjaž
Omladič
matjaz@omaldic.net
10.22034/aot.1611-1063
We present a new approach to sampling theory using the operator theory framework. We use a replacement operator and replace general frames of the sampling and reconstruction subspaces by normalized tight frames. The replacement can be done in a numerically stable and efficient way. The approach enables us to unify the standard consistent reconstruction results with the results for quasiconsistent reconstruction. Our approach naturally generalizes to consistent and quasiconsistent reconstructions from several samples. Not only we can handle sampling problems in a more efficient way, we also answer questions that seem to be open so far.
Sampling theory,consistent and quasiconsistent reconstructions,frames and normalized tight frames,replacement operator,several samples
http://www.aot-math.org/article_43335.html
http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
Reproducing pairs of measurable functions and partial inner product spaces
126
146
EN
Jean-Pierre
Antoine
Universit&eacute; catholique de Louvain - IRMP
jean-pierre.antoine@uclouvain.be
Camillo
Trapani
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
camillo.trapani@unipa.it
10.22034/aot.1611-1053
We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. <br />More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.
Reproducing pairs,continuous frames,upper and lower semi-frames,partial inner product spaces,lattices of Banach spaces
http://www.aot-math.org/article_43461.html
http://www.aot-math.org/article_43461_95adfe530628b355f4876073cbf601db.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
Some results about fixed points in the complete metric space of zero at infinity varieties and complete convex metric space of varieties
147
161
EN
Ghorban
Khalilzadeh Ranjbar
Bu_Ali Sina university
gh_khalilzadeh@yahoo.com
Tooraj
Amiri
t.amiri91@basu.ac.ir
10.22034/aot.1611-1050
This paper aims to study fixed points in the complete metric space of<br />varieties which are zero at infinity as a subspace of the complete metric space of all<br />varieties. Also, the convex structure of the complete metric space of all varieties<br />will be introduced.
Complete metric space,Variety,contractions,convexity,fixed point
http://www.aot-math.org/article_43478.html
http://www.aot-math.org/article_43478_a553260daef4ae543ab5e81d1f3d5f9b.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
Direct estimates of certain Mihesan-Durrmeyer type operators
162
178
EN
Arun
Kajla
Central University of Haryana, India
rachitkajla47@gmail.com
10.22034/aot.1612-1079
In this note we consider a Durrmeyer type operator having the basis functions in summation and integration due to Mihec{s}an [Creative Math. Inf. 17 (2008), 466--472.] and Pv{a}ltv{a}nea [Carpathian J. Math. 24 (2008), no. 3, 378--385.] that preserve the linear functions. We present a Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. In the last section of the paper, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation.
Positive approximation process,Rate of convergence,Modulus of continuity,Steklov mean
http://www.aot-math.org/article_43785.html
http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
2
2017
04
01
On spectral synthesis in several variables
179
191
EN
Laszlo
Szekelyhidi
University of Debrecen, Hungary
lszekelyhidi@gmail.com
10.22034/aot.1610-1028
In a recent paper we proposed a possible generalization of L. Schwartz's classical spectral synthesis result for continuous functions in several variables. The idea is based on Gelfand pairs and spherical functions while "translation invariance" is replaced by invariance with respect to the action of affine groups. In this paper we describe the function classes which play the role of the exponential monomials in this setting.
Gelfand pair,spherical function,spherical monomial,spectral synthesis
http://www.aot-math.org/article_44065.html
http://www.aot-math.org/article_44065_22554eff0c848ec4dfdef041770ec621.pdf