A Note on Supercyclic Operators in Locally Convex Spaces
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DOI: 10.1007/s00009-019-1386-y
Abstract: We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some… read more here.
Keywords: locally convex; convex spaces; note supercyclic; operators locally ... See more keywords
Lattice-equivalence of convex spaces
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DOI: 10.1007/s00012-019-0600-x
Abstract: The links between order and topology have been extensively studied. The objective of this paper is to study the similar links between convex spaces and order structures via the lattices of convex sets. In particular,… read more here.
Keywords: convex spaces; topology; equivalence convex; convex ... See more keywords
Orthogonality in locally convex spaces: Two nonlinear generalizations of Neumann's lemma
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DOI: 10.1016/j.jmaa.2019.123663
Abstract: Abstract In this note we prove a symmetric version of the Neumann lemma as well as a symmetric version of the Soderlind-Campanato lemma. We establish in this way two partial generalizations of the well-known Casazza-Christenses… read more here.
Keywords: two nonlinear; spaces two; orthogonality locally; convex spaces ... See more keywords
Fixed point theorems for countably asymptotically ะค-nonexpansive maps in locally convex spaces and application
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DOI: 10.2298/fil2003879b
Abstract: In this paper, we introduce the concept of a countably asymptotically ?-nonexpansive operator. In addition, we establish new fixed point results for some countably asymptotically ?-nonexpansive and sequentially continuous maps, fixed-point results of Krasnosel?skii type… read more here.
Keywords: convex spaces; asymptotically nonexpansive; locally convex; countably asymptotically ... See more keywords