ORIGINAL_ARTICLE
Some lower bounds for the numerical radius of Hilbert space operators
We show that if $T$ is a bounded linear operator on a complex Hilbert space, then\begin{equation*}\frac{1}{2}\Vert T\Vert\leq \sqrt{\frac{w^2(T)}{2} + \frac{w(T)}{2}\sqrt{w^2(T) - c^2(T)}} \leq w(T),\end{equation*}where $w(\cdot)$ and $c(\cdot)$ are the numerical radius and the Crawford number, respectively.We then apply it to prove that for each $t\in[0, \frac{1}{2})$ and natural number $k$,\begin{equation*}\frac{(1 + 2t)^{\frac{1}{2k}}}{{2}^{\frac{1}{k}}}m(T)\leq w(T),\end{equation*}where $m(T)$ denotes the minimum modulus of $T$. Some other related results are also presented.
http://www.aot-math.org/article_42504_e092353b73c1ef28452661188909e86f.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
98
107
10.22034/aot.1612-1076
Numerical radius
operator norm
Inequality
Cartesian decomposition
Ali
Zamani
zamani.ali85@yahoo.com
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
On maps compressing the numerical range between $C^*$-algebras
In this paper, we deal with the problem of characterizing linear maps compressing the numerical range. Acounterexample 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.
http://www.aot-math.org/article_43297_6b4eade500bac4d1f7c5e7db5bb95166.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
108
113
10.22034/aot.1612-1067
Numerical Range
C*-algebra, compressing the numerical range, Jordan *-homomorphism
Aschwag Fahad
Albideewi
msmabrouk@uqu.edu.sa
true
1
AUTHOR
Mohamed
Mabruk
mbs_mabrouk@yahoo.fr
true
2
FSG Tunisia
FSG Tunisia
FSG Tunisia
LEAD_AUTHOR
ORIGINAL_ARTICLE
Normalized tight vs. general frames in sampling problems
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.
http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
114
125
10.22034/aot.1611-1063
Sampling theory
consistent and quasiconsistent reconstructions
frames and normalized tight frames
replacement operator
several samples
Tomaž
Košir
tomaz.kosir@fmf.uni-lj.si
true
1
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
LEAD_AUTHOR
Matjaž
Omladič
matjaz@omaldic.net
true
2
AUTHOR
ORIGINAL_ARTICLE
Reproducing pairs of measurable functions and partial inner product spaces
We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. 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.
http://www.aot-math.org/article_43461_95adfe530628b355f4876073cbf601db.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
126
146
10.22034/aot.1611-1053
Reproducing pairs
continuous frames
upper and lower semi-frames
partial inner product spaces
lattices of Banach spaces
Jean-Pierre
Antoine
jean-pierre.antoine@uclouvain.be
true
1
Universit&eacute; catholique de Louvain - IRMP
Universit&eacute; catholique de Louvain - IRMP
Universit&eacute; catholique de Louvain - IRMP
LEAD_AUTHOR
Camillo
Trapani
camillo.trapani@unipa.it
true
2
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
AUTHOR
ORIGINAL_ARTICLE
Some results about fixed points in the complete metric space of zero at infinity varieties and complete convex metric space of varieties
This paper aims to study fixed points in the complete metric space ofvarieties which are zero at infinity as a subspace of the complete metric space of allvarieties. Also, the convex structure of the complete metric space of all varietieswill be introduced.
http://www.aot-math.org/article_43478_a553260daef4ae543ab5e81d1f3d5f9b.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
147
161
10.22034/aot.1611-1050
Complete metric space
variety
contractions
convexity
Fixed point
Ghorban
Khalilzadeh Ranjbar
gh_khalilzadeh@yahoo.com
true
1
Bu_Ali Sina university
Bu_Ali Sina university
Bu_Ali Sina university
LEAD_AUTHOR
Tooraj
Amiri
t.amiri91@basu.ac.ir
true
2
AUTHOR
ORIGINAL_ARTICLE
Direct estimates of certain Mihesan-Durrmeyer type operators
In this note we consider a Durrmeyer type operator having the basis functions in summation and integration due to Mihe\c{s}an [Creative Math. Inf. 17 (2008), 466--472.] and P\v{a}lt\v{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.
http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
162
178
10.22034/aot.1612-1079
Positive approximation process
rate of convergence
modulus of continuity
Steklov mean
Arun
Kajla
rachitkajla47@gmail.com
true
1
Central University of Haryana, India
Central University of Haryana, India
Central University of Haryana, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
On spectral synthesis in several variables
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.
http://www.aot-math.org/article_44065_22554eff0c848ec4dfdef041770ec621.pdf
2017-04-01T11:23:20
2017-11-18T11:23:20
179
191
10.22034/aot.1610-1028
Gelfand pair
spherical function
spherical monomial
spectral synthesis
Laszlo
Szekelyhidi
lszekelyhidi@gmail.com
true
1
University of Debrecen, Hungary
University of Debrecen, Hungary
University of Debrecen, Hungary
LEAD_AUTHOR