2017-11-18T20:56:03Z
http://www.aot-math.org/?_action=export&rf=summon&issue=4901
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
Some lower bounds for the numerical radius of Hilbert space operators
Ali
Zamani
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.
Numerical radius
operator norm
Inequality
Cartesian decomposition
2017
04
01
98
107
http://www.aot-math.org/article_42504_e092353b73c1ef28452661188909e86f.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
On maps compressing the numerical range between $C^*$-algebras
Aschwag Fahad
Albideewi
Mohamed
Mabruk
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.
Numerical Range
C*-algebra, compressing the numerical range, Jordan *-homomorphism
2017
04
01
108
113
http://www.aot-math.org/article_43297_6b4eade500bac4d1f7c5e7db5bb95166.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
Normalized tight vs. general frames in sampling problems
Tomaž
Košir
Matjaž
Omladič
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
2017
04
01
114
125
http://www.aot-math.org/article_43335_a0eb80054183c1d231c2f48925a39cca.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
Reproducing pairs of measurable functions and partial inner product spaces
Jean-Pierre
Antoine
Camillo
Trapani
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.
Reproducing pairs
continuous frames
upper and lower semi-frames
partial inner product spaces
lattices of Banach spaces
2017
04
01
126
146
http://www.aot-math.org/article_43461_95adfe530628b355f4876073cbf601db.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
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
Tooraj
Amiri
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.
Complete metric space
variety
contractions
convexity
Fixed point
2017
04
01
147
161
http://www.aot-math.org/article_43478_a553260daef4ae543ab5e81d1f3d5f9b.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
Direct estimates of certain Mihesan-Durrmeyer type operators
Arun
Kajla
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
2017
04
01
162
178
http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2017
2
2
On spectral synthesis in several variables
Laszlo
Szekelyhidi
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
2017
04
01
179
191
http://www.aot-math.org/article_44065_22554eff0c848ec4dfdef041770ec621.pdf