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Left-Invertibility of Rank-One Perturbations
For each isometry V acting on some Hilbert space and a pair of vectors f and g in the same Hilbert space, we associate a nonnegative number...
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Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem
In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In...
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Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our...
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Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces
This paper is devoted to studying the representation of measures of non-generalized compactness, in particular, measures of noncompactness, of...
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On the (non-)surjectivity of compact operators
First, a general method to construct compact surjective operators between infinite-dimensional normed spaces is given. Thereafter, a sufficient...
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Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure
In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff...
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Super weak compactness and uniform Eberlein compacta
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that...
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Convex Combinations of Weak*-Convergent Sequences and the Mackey Topology
A Banach space X is said to have property (K) if every w *-convergent sequence in X * admits a convex block subsequence which converges with respect to...
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On Caffarelli-Kohn-Nirenberg Inequalities for Block-Radial Functions
The paper provides weighted Sobolev inequalities of the Caffarelli-Kohn-Nirenberg type for functions with multi-radial symmetry. An elementary...
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On compact extensions of multilinear operators
In this paper we prove that, under certain conditions, Nicodemi extensions of compact multilinear operators between Banach spaces are compact as...
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Corrections to the paper “The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces”
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an...
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An alternative proof of the Aubin–Lions lemma
Using a generalized version of the Weyl–Riesz criterion for compactness of subsets of Lebesgue–Bochner spaces, we present in this short note an...
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A geometric criterion for compactness of invariant subspaces
Let M be a non-compact homogeneous Riemannian manifold, and let Ω be a compact subgroup of isometries of M . We show, under general conditions, that...
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Estimates for the topological degree and related topics
This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV...
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Concentration Analysis and Cocompactness
Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences....