Related papers: Lineability and modes of convergence
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
Given compact Lie groups H\subset G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…
We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behaviour of equi-Baire 1 and equi-Lebesgue families with respect to…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. In particular, it is shown that a…
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
We study asymmetric regular types. If $\frak p$ is regular and $A$-asymmetric then there exists a strict order such that Morley sequences in $\frak p$ over $A$ are strictly increasing (we allow Morley sequences to be indexed by elements of…
Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
Recently Tomasz Natkaniec in [On lineability of families of non-measurable functions of two variable. Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM, 115(1):Paper No. 33, 10, 2021] studied the lineability problem for several…
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S^2xR^3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the…
Problems in econometrics, insurance, reliability engineering, and statistics quite often rely on the assumption that certain functions are non-decreasing. To satisfy this requirement, researchers frequently model the underlying phenomena…
We give some experimental observations on the growth of the norm of certain matrices related to the Mertens function. The results obtained in these experiments convince us that linear algebra may help in the study of Mertens function and…