Sufficient conditions for the differentiability of mappings of locally convex spaces

1986 ◽  
Vol 39 (1) ◽  
pp. 39-46
Author(s):  
S. G. Lobanov
Keyword(s):  
Sufficient Conditions ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Regularization of cylindrical processes in locally convex spaces

2020 ◽  
pp. 2050027
Author(s):  
Christian A. Fonseca-Mora
Keyword(s):  
Convex Space ◽  
Lévy Process ◽  
Sufficient Conditions ◽  
Locally Convex Space ◽  
Levy Process ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Strong Dual ◽  
Convex Spaces

Let [Formula: see text] be a locally convex space and let [Formula: see text] denote its strong dual. In this paper, we introduce sufficient conditions for the existence of a continuous or a càdlàg [Formula: see text]-valued version to a cylindrical process defined on [Formula: see text]. Our result generalizes many other known results on the literature and their different connections will be discussed. As an application, we provide sufficient conditions for the existence of a [Formula: see text]-valued càdlàg Lévy process version to a given cylindrical Lévy process in [Formula: see text].

scholarly journals On Homomorphisms, Open Operators and their Adjoints

2001 ◽  
Vol 8 (4) ◽  
pp. 823-844
Author(s):  
D. Zarnadze
Keyword(s):  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Locally Convex Spaces ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Convex Spaces

Abstract The well-known A. Grothendieck's theorem on a homomorphism between locally convex spaces is generalized to the case of topologies which are incompatible with dualities. On the basis of this theorem, necessary and sufficient conditions are obtained for a weak homomorphism (resp. its adjoint operator, resp. its double adjoint operator) to be again a homomorphism in various topologies of the initial (resp. dual, resp. bidual) spaces. Some new classes of pairs of locally convex spaces satisfying these conditions are established. The results obtained have enabled us to reveal new properties of frequently encountered homomorphisms and weakly open operators, as well as to strengthen and generalize some well-known results.

An Inverse Mapping Theorem in Frechet Spaces

1986 ◽  
Vol 29 (2) ◽  
pp. 238-245
Author(s):  
Henri-François Gautrin ◽  
Khaldoun Imam ◽  
Tapio Klemola ◽  
Jean-Marc Terrier
Keyword(s):  
Sufficient Conditions ◽  
Locally Convex Spaces ◽  
Fréchet Spaces ◽  
Inverse Mapping ◽  
Inverse Mapping Theorem ◽  
Locally Convex ◽  
Convex Spaces

AbstractWithin the framework of a-differentiability, introduced by H. R. Fischer in locally convex spaces, sufficient conditions for an inverse mapping theorem between Fréchet spaces are established.

scholarly journals Necessary and sufficient conditions for precompact sets to be metrisable

2006 ◽  
Vol 74 (1) ◽  
pp. 7-13 ◽  
Author(s):  
J.C. Ferrando ◽  
J. Kasakol ◽  
M. López Pellicer
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Locally Convex Spaces ◽  
Compact Sets ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Convex Spaces ◽  
Compact Subsets

This self-contained paper characterises those locally convex spaces whose (weakly) precompact (respectively, compact) subsets are metrisable. Applications and examples are provided. Our approach also applies to get Cascales-Orihuela's, Valdivia's and Robertson's metrisation theorems for (pre)compact sets.

Abstract time-fractional equations: Existence and growth of solutions

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Marko Kostić
Keyword(s):  
Sufficient Conditions ◽  
Existence Theory ◽  
Locally Convex Spaces ◽  
Growth Order ◽  
Fractional Equations ◽  
Locally Convex ◽  
Resolvent Families ◽  
Growth Of Solutions ◽  
Convex Spaces

AbstractWe contribute to the existence theory of abstract time-fractional equations by stating the sufficient conditions for generation of not exponentially bounded α-times C-regularized resolvent families (α > 1) in sequentially complete locally convex spaces. We also consider the growth order of constructed solutions.

scholarly journals On super efficiency in set-valued optimisation in locally convex spaces

2005 ◽  
Vol 71 (2) ◽  
pp. 183-192 ◽  
Author(s):  
Yihong Xu ◽  
Chuanxi Zhu
Keyword(s):  
Convex Sets ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Separation Theorem ◽  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Super Efficiency ◽  
Locally Convex ◽  
Convex Spaces

The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain its super efficient solutions are obtained. Also, Kuhn-Tucker and Lagrange sufficient conditions are derived. Finally two kinds of unconstrained programs equivalent to set-valued optimisation problems are established.

ON THE PRINCIPLE OF UNIFORM BOUNDEDNESS FOR LSC CONVEX PROCESSES IN A STRICTLY N LOCALLY CONVEX SPACES

2008 ◽  
Vol 41 (1) ◽  
Author(s):  
S. Lahrech ◽  
A. Jaddar ◽  
J. Hlal ◽  
A. Ouahab ◽  
A. Mbarki
Keyword(s):  
Uniform Boundedness ◽  
Locally Convex Spaces ◽  
Convex Processes ◽  
Locally Convex ◽  
Convex Spaces
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