eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
98
107
10.22034/aot.1612-1076
42504
Some lower bounds for the numerical radius of Hilbert space operators
Ali Zamani
zamani.ali85@yahoo.com
1
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.
http://www.aot-math.org/article_42504_e092353b73c1ef28452661188909e86f.pdf
Numerical radius
operator norm
inequality
Cartesian decomposition
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
108
113
10.22034/aot.1612-1067
43297
On maps compressing the numerical range between $C^*$-algebras
Aschwag Fahad Albideewi
msmabrouk@uqu.edu.sa
1
Mohamed Mabruk
mbs_mabrouk@yahoo.fr
2
FSG Tunisia
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.
http://www.aot-math.org/article_43297_6b4eade500bac4d1f7c5e7db5bb95166.pdf
Numerical Range
C*-algebra, compressing the numerical range, Jordan *-homomorphism
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
114
125
10.22034/aot.1611-1063
43335
Normalized tight vs. general frames in sampling problems
Tomaž Košir
tomaz.kosir@fmf.uni-lj.si
1
Matjaž Omladič
matjaz@omaldic.net
2
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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
Sampling theory
consistent and quasiconsistent reconstructions
frames and normalized tight frames
replacement operator
several samples
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
126
146
10.22034/aot.1611-1053
43461
Reproducing pairs of measurable functions and partial inner product spaces
Jean-Pierre Antoine
jean-pierre.antoine@uclouvain.be
1
Camillo Trapani
camillo.trapani@unipa.it
2
Universit&eacute; catholique de Louvain - IRMP
Dipartimento di Matematica e Informatica, Universit`a di Palermo
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.
http://www.aot-math.org/article_43461_95adfe530628b355f4876073cbf601db.pdf
Reproducing pairs
continuous frames
upper and lower semi-frames
partial inner product spaces
lattices of Banach spaces
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
147
161
10.22034/aot.1611-1050
43478
Some results about fixed points in the complete metric space of zero at infinity varieties and complete convex metric space of varieties
Ghorban Khalilzadeh Ranjbar
gh_khalilzadeh@yahoo.com
1
Tooraj Amiri
t.amiri91@basu.ac.ir
2
Bu_Ali Sina university
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.
http://www.aot-math.org/article_43478_a553260daef4ae543ab5e81d1f3d5f9b.pdf
Complete metric space
Variety
contractions
convexity
fixed point
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
162
178
10.22034/aot.1612-1079
43785
Direct estimates of certain Mihesan-Durrmeyer type operators
Arun Kajla
rachitkajla47@gmail.com
1
Central University of Haryana, India
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.
http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf
Positive approximation process
Rate of convergence
Modulus of continuity
Steklov mean
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2017-04-01
2
2
179
191
10.22034/aot.1610-1028
44065
On spectral synthesis in several variables
Laszlo Szekelyhidi
lszekelyhidi@gmail.com
1
University of Debrecen, Hungary
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
Gelfand pair
spherical function
spherical monomial
spectral synthesis