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Locally Convex Spaces
This chapter starts recalling the definitions of Hausdorff topological space, metric space, and normed space. Examples of Banach sequence spaces, of...
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Locally Convex Spaces
Recall that Theorems 2.6.4 and 2.6.7 established the HB...
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Locally Convex Spaces with All Archimedean Cones Closed
We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of...
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Concepts of almost periodicity and ergodic theorems in locally convex spaces
We wish to investigate mean ergodic theorems for generalizations of almost periodic functions on semigroups, as well as for semigroups of operators...
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Lagrange Multipliers in Locally Convex Spaces
We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many...
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The b-Gelfand–Phillips property for locally convex spaces
We extend the well-known Gelfand–Phillips property for Banach spaces to locally convex spaces, defining a locally convex space E to be b -Gelfand–Phill...
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Locally convex spaces with the strong Gelfand–Phillips property
We introduce the strong Gelfand–Phillips property for locally convex spaces and give several characterizations of this property. We characterize the...
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The abstract Cauchy problem in locally convex spaces
We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff...
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Topological duals of locally convex function spaces
This paper studies topological duals of locally convex function spaces that are natural generalizations of Fréchet and Banach function spaces. The...
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The locally k-uniformly extremely convex and midpoint locally k-uniformly extremely convex Banach spaces
The locally k -uniformly extremely convex Banach spaces are introduced. It is shown here that every locally k -uniformly extremely convex space is...
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Continuous Fréchet Differentiability of the Moreau Envelope of Convex Functions on Banach Spaces
It is shown that the Moreau envelope of a convex lower semicontinuous function on a real Banach space with strictly convex dual is Fréchet...
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Non-existing and ill-behaved coequalizers of locally ordered spaces
Categories of locally ordered spaces are especially well-adapted to the realization of most precubical sets, although their colimits are not so easy...
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Partially defined operators on locally Hilbert spaces
We investigate partially defined operators on inductive limits of Hilbert spaces, in order to introduce an operator theory for a class of linear...
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Locally uniformly convex renorming of nonseparable spaces
This chapter deals with renormings —for the main part, LUR renormings— of the more “accessible” nonseparable Banach spaces (weakly compactly...