Some lower bounds for the numerical radius of Hilbert space operators
Ali
Zamani
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
98
107
http://www.aot-math.org/article_42504_e092353b73c1ef28452661188909e86f.pdf
dx.doi.org/10.22034/aot.1612-1076
On maps compressing the numerical range between $C^*$-algebras
Aschwag Fahad
Albideewi
author
Mohamed
Mabruk
FSG Tunisia
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
108
113
http://www.aot-math.org/article_43297_6b4eade500bac4d1f7c5e7db5bb95166.pdf
dx.doi.org/10.22034/aot.1612-1067
Normalized tight vs. general frames in sampling problems
Tomaž
Košir
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
author
Matjaž
Omladič
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
114
125
http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf
dx.doi.org/10.22034/aot.1611-1063
Reproducing pairs of measurable functions and partial inner product spaces
Jean-Pierre
Antoine
Universit&eacute; catholique de Louvain - IRMP
author
Camillo
Trapani
Dipartimento di Matematica e Informatica,
Universit`a di Palermo
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
126
146
http://www.aot-math.org/article_43461_95adfe530628b355f4876073cbf601db.pdf
dx.doi.org/10.22034/aot.1611-1053
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
Bu_Ali Sina university
author
Tooraj
Amiri
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
147
161
http://www.aot-math.org/article_43478_a553260daef4ae543ab5e81d1f3d5f9b.pdf
dx.doi.org/10.22034/aot.1611-1050
Direct estimates of certain Mihesan-Durrmeyer type operators
Arun
Kajla
Central University of Haryana, India
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
162
178
http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf
dx.doi.org/10.22034/aot.1612-1079
On spectral synthesis in several variables
Laszlo
Szekelyhidi
University of Debrecen, Hungary
author
text
article
2017
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
2
v.
2
no.
2017
179
191
http://www.aot-math.org/article_44065_22554eff0c848ec4dfdef041770ec621.pdf
dx.doi.org/10.22034/aot.1610-1028