相关论文: Banach SSD spaces and classes of monotone sets

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions.

In this paper, we develop some of the theory of SSD spaces and SSDB spaces, and deduce some results on maximally monotone multifunctions on a reflexive Banach space.

In this paper we introduce the notion of enlargement of a positive set in SSD spaces. To a maximally positive set $A$ we associate a family of enlargements $\E(A)$ and characterize the smallest and biggest element in this family with…

We give, for general Banach spaces, a characterization of the sequential lower limit of maximal monotone operators of type (D) and prove its representability. As a consequence, using a recent extension of the Moreau-Yosida regularization…

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable…

We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach…

Gossez type (D) operators are defined in non-reflexive Banach spaces and share with the subdifferential a topological related property, characterized by bounded nets. In this work we present new properties and characterizations of these…

We prove that the norm of $X\widehat{\otimes}_\pi Y$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q<p$ (e.g. if $Y^*$ is a subspace of $L_q$) or…

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

This paper is about the maximally monotone and quasidense subsets of the product of a real Banach space and its dual. We discuss six subclasses of the maximal monotone sets that are equivalent to the quasidense ones. We define the Gossez…

Recently in [1] a new class of maximal monotone operators has been introduced. In this note we study domain range properties as well as connections with other classes and calculus rules for these operators we called strongly-representable.…

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

It is well known that weakly $p$-summable sequences in a Banach space $E$ are associated to bounded operators from $\ell_{p^*}$ to $E$, and unconditionally $p$-summable sequences in $E$ are associated to compact operators from $\ell_{p^*}$…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we…

The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n, there is a definable type p in X, definable over a code for…

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a…

This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We…

In this paper, we show how the Brezis-Browder theorem for maximally monotone multifunctions with a linear graph on a reflexive Banach space, and a consequence of it due to Yao, can be generalized to SSDB spaces.

In this paper we consider the "quasidensity" of a subset of the product of a Banach space and its dual, and give a connection between quasidense sets and sets of "type (NI)". We discuss "coincidence sets" of certain convex functions and…