Related papers: A Sum Theorem for (FPV) Operators and Normal Cones
A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11
The main purpose of this paper is to correct an error in the previously submitted version [*] := arXiv:2004.13749v1. [*] had been already accepted for publication in a scientific journal, but withdrawn by the author after the discovery of…
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
In this note we solve, except for extremely pathological cases, a question posed by Puglisi and Seoane-Sepulveda on the lineability of the set of bounded non-absolutely summing linear operators. We also show how the idea of the proof can be…
In this paper we present a short and elementary proof for the error in Simpson's rule.
Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression,…
Recent work by Pain [1] proposed a systematic approach to evaluating binomial sums involving reciprocals of binomial coefficients via Beta integrals. In particular, a parametric extension (Proposition 6.1) was introduced and claimed to…
We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van Lambalgen's theorem for Schnorr randomness.…
We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.
In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these…
The purpose of this note is make Theorem 13 in the article "On Biautomaticity of Non-Homogenous Small-Cancellation Groups" more accessible. Restatements of the theorem already appeared in few of the authors' succeeding works but with no…
This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
This is an erratum to our paper.
This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.