Series representations in spaces of vector‐valued functions via Schauder decompositions
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DOI: 10.1002/mana.201900172
Abstract: It is a classical result that every C ‐valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E… read more here.
Keywords: locally convex; series; valued functions; schauder decompositions ... See more keywords
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
On the strict, uniform and compact-open topologies on an algebra
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DOI: 10.1007/s10998-017-0229-5
Abstract: We introduce and study strict, uniform, and compact-open locally convex topologies on an algebra $${\mathcal {B}},$$B, by the fundamental system of seminorms of a locally convex subalgebra $$({\mathcal {A},p}_\alpha )$$(A,pα). Moreover, we investigate when $${\mathcal… read more here.
Keywords: compact open; topologies algebra; uniform compact; strict uniform ... See more keywords
Some Notes on Barreledness in Locally Convex Cones
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DOI: 10.1007/s41980-020-00519-x
Abstract: In this paper, we verify a relation between the symmetric continuity of lower semicontinuous extended seminorms on a locally convex cone with respect to the symmetric topology and barreledness of the locally convex cone. The… read more here.
Keywords: locally convex; convex cones; convex cone; notes barreledness ... 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
COMPATIBLE LOCALLY CONVEX TOPOLOGIES ON NORMED SPACES: CARDINALITY ASPECTS
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DOI: 10.1017/s0004972717000090
Abstract: For a normed infinite-dimensional space, we prove that the family of all locally convex topologies which are compatible with the original norm topology has cardinality greater or equal to c. read more here.
Keywords: locally convex; convex topologies; normed spaces; cardinality ... See more keywords
Fixed point theorems for countably asymptotically Ф-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
A locally Convex Topology on the Beurling Algebras
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DOI: 10.29252/mmr.5.2.221
Abstract: Introduction Let G be a locally compact group with a fixed left Haar measure λ and be a weight function on G; that is a Borel measurable function with for all . We denote by… read more here.
Keywords: locally convex; medicine; beurling algebras; topology beurling ... See more keywords