Collectanea Mathematica
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A version of Kalton’s theorem for the space of regular operators
Collectanea Mathematica - Tập 66 - Trang 55-62 - 2014
In this note we extend some recent results in the space of regular operators [appeared in Bu and Wong (Indag Math 23:199–213, 2012), Bu et al. (Collect Math 62:131–137, 2011), and Li et al. (Taiwan J Math 16:207–215, 2012)]. Our main result is the following Banach lattice version of a classical result of Kalton: Let
$$E$$
......
On existence of solutions of a neutral differential equation with deviating argument
Collectanea Mathematica - Tập 61 - Trang 37-47 - 2010
We establish theorems on the existence and asymptotic characterization of solutions of a differential equation of neutral type with deviated argument on neutral type. The mentioned differential equation admits both delayed and advanced arguments. In our considerations we use technique linking measures of noncompactness with the Tikhonov fixed point principle in suitable Frechet space. This approac......
Halfspace type theorems for self-shrinkers in arbitrary codimension
Collectanea Mathematica - - Trang 1-11 - 2023
In this paper, we generalize some halfspace type theorems for self-shrinkers of codimension 1 to the case of arbitrary codimension.
Well-posedness in weighted Sobolev spaces for elliptic equations of Cordes type
Collectanea Mathematica - Tập 67 - Trang 539-554 - 2015
In this paper we prove some weighted
$$W^{2,2}$$
-a priori bounds for a class of linear, elliptic, second-order, differential operators of Cordes type in certain weighted Sobolev spaces on unbounded open sets
......
Existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional $$p\left( .,.\right)$$ -Laplacian operator in $${\mathbb {R}}^{N}$$
Collectanea Mathematica - Tập 72 - Trang 129-156 - 2020
In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional
$$p\left( .,.\right)$$
-Laplacian in fractional Sobolev space with variable ex......
Comparison theorems for deformation functors via invariant theory
Collectanea Mathematica - Tập 70 Số 1 - Trang 1-32 - 2019
Some results concerning ideal and classical uniform integrability and mean convergence
Collectanea Mathematica - Tập 74 - Trang 1-25 - 2021
In this article, the concept of
$${\mathcal {J}}$$
-uniform integrability of a sequence of random variables
$$\left\{ X_{k}\right\} $$
with respect to
......
On the local integrability condition for generalised translation-invariant systems
Collectanea Mathematica - Tập 70 - Trang 407-429 - 2019
This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calderón integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions for satisfying the local integrability condition are closely related to lower and upper bounds on the number of lattice point......
Polynomial ring representations of endomorphisms of exterior powers
Collectanea Mathematica - Tập 73 - Trang 107-133 - 2021
An explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approxima......
On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space
Collectanea Mathematica - Tập 73 - Trang 521-533 - 2021
We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space
$$\mathcal {X}$$
. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on
$$\mathca......
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