2017
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Some lower bounds for the numerical radius of Hilbert space operators
2
2
We show that if $T$ is a bounded linear operator on a complex Hilbert space, thenbegin{equation*}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),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 $tin[0, frac{1}{2})$ 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.
1

98
107


Ali
Zamani
Iran
zamani.ali85@yahoo.com
Numerical radius
operator norm
inequality
Cartesian decomposition
On maps compressing the numerical range between $C^*$algebras
2
2
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.
1

108
113


Aschwag Fahad
Albideewi
Saudi Arabia
msmabrouk@uqu.edu.sa


Mohamed
Mabruk
FSG Tunisia
FSG Tunisia
Tunisia
mbs_mabrouk@yahoo.fr
Numerical Range
C*algebra, compressing the numerical range, Jordan *homomorphism
Normalized tight vs. general frames in sampling problems
2
2
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.
1

114
125


Tomaž
Košir
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI1000 Ljubljana, Slovenia
Faculty of Mathematics and Physics, University
Slovenia
tomaz.kosir@fmf.unilj.si


Matjaž
Omladič
Slovenia
matjaz@omaldic.net
Sampling theory
consistent and quasiconsistent reconstructions
frames and normalized tight frames
replacement operator
several samples
Reproducing pairs of measurable functions and partial inner product spaces
2
2
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.
1

126
146


JeanPierre
Antoine
Universit&eacute; catholique de Louvain  IRMP
Universit&eacute; catholique de Louvain
Belgium
jeanpierre.antoine@uclouvain.be


Camillo
Trapani
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
Dipartimento di Matematica e Informatica,
Universi
Italy
camillo.trapani@unipa.it
Reproducing pairs
continuous frames
upper and lower semiframes
partial inner product spaces
lattices of Banach spaces
Some results about fixed points in the complete metric space of zero at infinity varieties and complete convex metric space of varieties
2
2
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.
1

147
161


Ghorban
Khalilzadeh Ranjbar
Bu_Ali Sina university
Bu_Ali Sina university
Iran
gh_khalilzadeh@yahoo.com


Tooraj
Amiri
Iran
t.amiri91@basu.ac.ir
Complete metric space
Variety
contractions
convexity
fixed point
Direct estimates of certain MihesanDurrmeyer type operators
2
2
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), 466472.] and Pv{a}ltv{a}nea [Carpathian J. Math. 24 (2008), no. 3, 378385.] 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.
1

162
178


Arun
Kajla
Central University of Haryana, India
Central University of Haryana, India
India
rachitkajla47@gmail.com
Positive approximation process
rate of convergence
modulus of continuity
Steklov mean
On spectral synthesis in several variables
2
2
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.
1

179
191


Laszlo
Szekelyhidi
University of Debrecen, Hungary
University of Debrecen, Hungary
Hungary
lszekelyhidi@gmail.com
Gelfand pair
spherical function
spherical monomial
spectral synthesis