Related papers: On the paper "statistical approximation by positiv…
In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].
Error in proof of theorem 10.
We prove some refinements of a reverse AM-GM operator inequality due to M. Lin [Studia Math. 2013;215:187-194]. In particular, we show the operator inequality \begin{eqnarray*} \Phi^p\left(A\nabla_\nu B+2rMm(A^{-1}\nabla B^{-1}-A^{-1}\sharp…
This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
John Morgan and G,Tian pointed out a mistake in the concluding argument for our paper entitled "$C_1$ in [2] is zero", which was recently published in arXiv:1512.02098. We hereby acknowledge this mistake and correct the computation, leading…
We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in 1/(\ell+1/2). This extended Limber approximation can be used to test the accuracy of the…
This is an erratum to the article: "Computation of maximal projection constants" (J. Funct. Anal., 277). The statement of Lemma 3.1(2) of that paper is incorrect. As a consequence of this the proof of Theorem 1.4 is incomplete. In this…
We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13].
Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. In this note, we show that a lemma used in the proof of the main result of [ Taghavi and Hosseinzadeh, linear and…
Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and consequently give the modified results.
Let $A,B\in \mathbb{B}(\mathscr{H})$ be such that $0<b_{1}I \leq A \leq a_{1}I$ and $0<b_{2}I \leq B \leq a_{2}I$ for some scalars $0<b_{i}< a_{i},\;\; i=1,2$ and $\Phi:\mathbb{B}(\mathscr{H})\rightarrow\mathbb{B}(\mathscr{K})$ be a…
We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…
In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…
This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.
We correct an inaccuracy in the original proof
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that reproduce the logarithmic function $\ln(1+\mu+x)$, with $\mu >…
Among other things, it is shown that there exist Banach spaces $Z$ and $W$ such that $Z^{**}$ and $W$ have bases, and for every $p\in[1,2)$ there is an operator $T:W\to Z$ that is not $p$-nuclear but $T^{**}$ is $p$-nuclear.
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…