M. Raja
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View article: Covering $$B_X$$ by finitely many convex sets
Covering $$B_X$$ by finitely many convex sets Open
Given a finite covering by closed convex sets of $$B_X$$ , the unit ball of an infinite-dimensional Banach space, we investigate whether there is a set of the covering that contains balls of radius close to 1 and (a) arbitrarily high f…
View article: Chaos, Local Dynamics, Codimension-One and Codimension-Two Bifurcation Analysis of a Discrete Predator–Prey Model with Holling Type I Functional Response
Chaos, Local Dynamics, Codimension-One and Codimension-Two Bifurcation Analysis of a Discrete Predator–Prey Model with Holling Type I Functional Response Open
We explore chaos, local dynamics, codimension-one, and codimension-two bifurcations of an asymmetric discrete predator–prey model. More precisely, for all the model’s parameters, it is proved that the model has two boundary fixed points an…
View article: Covering $B_X$ by finitely many convex sets
Covering $B_X$ by finitely many convex sets Open
Given a finite covering by closed convex sets of $B_X$, the unit ball of an infinite-dimensional Banach space, we investigate whether there is a set of the covering that contains balls of radius close to $1$ and (a) arbitrarily high finite…
View article: Representation in $C(K)$ by Lipschitz functions
Representation in $C(K)$ by Lipschitz functions Open
The isometric universality of the spaces $C(K)$ for $K$ a non scattered Hausdorff compact does not take into account the ``quality'' of the representation. Indeed, the existence of an isometric copy of a separable Banach space $X$ into $C(…
View article: Topologies related to (I)-envelopes
Topologies related to (I)-envelopes Open
We investigate the question whether the (I)-envelope of any subset of a dual to a Banach space $X$ may be described as the closed convex hull in a suitable topology. If $X$ contains no copy of $\ell^1$ then the weak topology generated by f…
View article: Subspaces of Hilbert-generated Banach spaces and the quantification of super weak compactness
Subspaces of Hilbert-generated Banach spaces and the quantification of super weak compactness Open
We introduce a measure of super weak noncompactness Γ defined for bounded subsets and bounded linear operators in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert-generat…
View article: Ergodicity and super weak compactness
Ergodicity and super weak compactness Open
We prove that a closed convex subset of a Banach space is (super-)weakly compact if and only if it is (super)-ergodic. As a consequence we deduce that super weakly compact sets are characterized by the fixed point property for continuous a…
View article: Nonlinear aspects of super weakly compact sets
Nonlinear aspects of super weakly compact sets Open
The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu [32] which establishes that the closed con…
View article: Applications of the quantification of super weak compactness
Applications of the quantification of super weak compactness Open
We introduce a measure of super weak noncompactness $Γ$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated spa…
View article: On strong asymptotic uniform smoothness and convexity
On strong asymptotic uniform smoothness and convexity Open
We introduce the notions of strong asymptotic uniform smoothness and convexity. We show that the injective tensor product of strongly asymptotically uniformly smooth spaces is asymptotically uniformly smooth. This applies in particular to …
View article: Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces
Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces Open
In this note, we extend to the setting of quasi-reflexive spaces a classical result of N. Kalton and L. Randrianarivony on the coarse Lipschitz structure of reflexive and asymptotically uniformly smooth Banach spaces. As an application, we…
View article: WEAKLY METRIZABILITY OF SPHERES AND RENORMINGS OF BANACH SPACES
WEAKLY METRIZABILITY OF SPHERES AND RENORMINGS OF BANACH SPACES Open
We study the metrizability of weak topologies when restricted to the unit sphere of some equivalent norm on a Banach space, and its relationships with other geometrical properties of norms. In case of dual Banach space $X^{\\ast },$ we pro…
View article: Compact convex sets that admit a lower semicontinuous strictly convex function
Compact convex sets that admit a lower semicontinuous strictly convex function Open
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…
View article: Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces Open
We show that in a super-reflexive Banach space, the conditionality constants kN() of a quasi-greedy basis grow at most like O((logN) for some This extends results by the third-named author and Wojtaszczyk (2014), where this property was sh…