A CONTINUOUS LINEAR REPRESENTATION FROM A TOPOLOGICAL QUOTIENT GROUP INTO A TOPOLOGICAL QUOTIENT VECTOR SPACE

2020 ◽  
pp. 101-110
Author(s):  
Diah Junia Eksi Palupi
Keyword(s):  
Vector Space ◽  
Quotient Group ◽  
Linear Representation ◽  
Continuous Linear

scholarly journals Semi-embeddings of Banach spaces which are hereditarily c0

1983 ◽  
Vol 26 (2) ◽  
pp. 163-167 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Closed Unit Ball ◽  
Continuous Linear ◽  
Scattered Space ◽  
Complete Set

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

scholarly journals On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1061-1068
Author(s):  
Seda Öztürk
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Integral Representation ◽  
Unit Circle ◽  
Banach Spaces ◽  
Fourier Coefficients ◽  
Linear Representation ◽  
Complex Banach Space ◽  
Continuous Linear

In this paper, for an isometric strongly continuous linear representation denoted by ? of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A?r (x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A?r and ?.

Linearization of a Contractive Homeomorphism

1968 ◽  
Vol 20 ◽  
pp. 1387-1390
Author(s):  
Ludvik Janos
Keyword(s):  
Linear Operator ◽  
Topological Space ◽  
Vector Space ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Topological Embedding

Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

ANDERSÉN–LEMPERT-THEORY WITH PARAMETERS: A REPRESENTATION THEORETIC POINT OF VIEW

2005 ◽  
Vol 04 (03) ◽  
pp. 325-340 ◽  
Author(s):  
FRANK KUTZSCHEBAUCH
Keyword(s):  
Vector Space ◽  
Vector Fields ◽  
Invariant Subspaces ◽  
Linear Representation ◽  
Complex Variables ◽  
Point Of View ◽  
Several Complex Variables ◽  
Algebraic Vector ◽  
Theoretic Point ◽  
Parametric Version

We calculate the invariant subspaces in the linear representation of the group of algebraic automorphisms of ℂnon the vector space of algebraic vector fields on ℂnand more generally we do this in a setting with parameter. As an application to the field of Several Complex Variables we get a new proof of the Andersén–Lempert observation and a parametric version of the Andersén–Lempert theorem. Further applications to the question of embeddings of ℂkinto ℂnare announced.

Groups definable in ordered vector spaces over ordered division rings

2007 ◽  
Vol 72 (4) ◽  
pp. 1108-1140 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Sergei Starchenko
Keyword(s):  
Fundamental Group ◽  
Vector Space ◽  
Division Ring ◽  
Quotient Group ◽  
Vector Spaces ◽  
Division Rings ◽  
Ordered Vector Space ◽  
Dimensional Group ◽  
Ordered Vector Spaces

AbstractLet M = 〈M, +, <, 0, {λ}λЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.

On the Convergence Vector Space ℒ,(E, F) and its Dual Space

1978 ◽  
Vol 21 (3) ◽  
pp. 279-284 ◽  
Author(s):  
Ronald Beattie
Keyword(s):  
Vector Space ◽  
Normed Space ◽  
Dual Space ◽  
Continuous Mapping ◽  
Continuous Linear ◽  
Continuous Convergence ◽  
Convergence Structure ◽  
Locally Convex

Let E be a locally convex tvs, F a normed space and the space of continuous linear mappings from E into F In this paper, we investigate the continuous convergence structure (c-structure) on. denotes the resulting convergence vector space (cvs).The c-structure is by definition the coarsest cvs structure on making evaluation a continuous mapping.

On Convergence of Projections in Locally Convex Spaces

1966 ◽  
Vol 9 (1) ◽  
pp. 107-110
Author(s):  
J. E. Simpson
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Linear Mapping ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Continuous Linear Mapping ◽  
Basic Assumptions ◽  
Locally Convex ◽  
Strong Dual ◽  
Convex Spaces

This note is concerned with the extension to locally convex spaces of a theorem of J. Y. Barry [ 1 ]. The basic assumptions are as follows. E is a separated locally convex topological vector space, henceforth assumed to be barreled. E' is its strong dual. For any subset A of E, we denote by w(A) the closure of A in the σ-(E, E')-topology. See [ 2 ] for further information about locally convex spaces. By a projection we shall mean a continuous linear mapping of E into itself which is idempotent.

Bounded-weak topologies and completeness in vector spaces

1953 ◽  
Vol 49 (2) ◽  
pp. 183-189
Author(s):  
G. T. Roberts
Keyword(s):  
Linear System ◽  
Vector Space ◽  
Weak Topology ◽  
Vector Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Bounded Set ◽  
Weakly Continuous ◽  
Weak Topologies

Suppose that X is any vector space on which it is possible to recognize a class of sets of such a nature that it is natural to call them ‘bounded’. (Precise conditions for such a class of sets are given in § 2.) Let L be any vector space of linear functionals on X which map each ‘bounded’ set into a bounded set. We say that a filter is boundedly-weakly convergent if it is convergent in the weak topology of the linear system [X, L] and contains a ‘bounded’ set. If M is a vector space of boundedly-weakly continuous linear functionals on X which includes L, we say that a subset S of M is limited if 〈 , f〉 converges uniformly for f ε S whenever is a boundedly-weakly convergent filter.

scholarly journals On the semigroup of all continuous linear mappings on a Banach space

1971 ◽  
Vol 4 (2) ◽  
pp. 201-203
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Real Vector Space ◽  
Continuous Linear ◽  
Real Vector ◽  
Linear Transformations

It is veil-known that every ring automorphism of the ring of all linear transformations of a real vector space into itself is inner. We shall show that, if this ring is regarded as a semigroup with respect to composition and the dimension of the vector space is not less than 2, every semigroup automorphism is inner.

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