A representation theory of continuous linear maps

1964 ◽  
Vol 155 (4) ◽  
pp. 270-291 ◽  
Author(s):  
Khyson Swong
Keyword(s):  
Representation Theory ◽  
Continuous Linear ◽  
Linear Maps

Continuous Linear Maps

2014 ◽  
pp. 115-138
Author(s):  
Joseph Muscat
Keyword(s):  
Continuous Linear ◽  
Linear Maps

scholarly journals On the surjectivity of linear maps on locally convex spaces

1982 ◽  
Vol 32 (2) ◽  
pp. 187-211 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Basic Notion ◽  
Linear Map ◽  
Linear Maps ◽  
Locally Convex ◽  
Do So ◽  
Convex Spaces

AbstractThe aim of this note is to investigate the structure of general surjectivity problem for a continuous linear map between locally convex spaces. We shall do so by using the method introduced in Yamamuro (1980). Its basic notion is that of calibrations which has been introduced in Yamamuro (1975), studied in detail in Yamamuro (1979) and appliced to several problems in Yamamuro (1978) and Yamamuro (1979a).

scholarly journals Pitt's theorem for operators between general Lorentz sequence spaces

2002 ◽  
Vol 90 (1) ◽  
pp. 101 ◽  
Author(s):  
J. A. López Molina
Keyword(s):  
Sequence Spaces ◽  
Continuous Linear ◽  
Linear Maps ◽  
Pitt’S Theorem

We characterize the pairs of general Lorentz sequence spaces $\ell^{u,v}(\nu),$ $\ell^{p,q}(\mu), 0 < u, v, p, q < \infty$ such that all continuous linear maps from the first space into the second one are compact.

scholarly journals The Chromatic Brauer Category and Its Linear Representations

2020 ◽  
Author(s):  
L. Felipe Müller ◽  
Dominik J. Wrazidlo
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Topological Field Theories ◽  
Monoidal Category ◽  
Field Theories ◽  
Vector Spaces ◽  
Real Vector ◽  
Linear Representations ◽  
Linear Maps ◽  
Topological Field

AbstractThe Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category are symmetric strict monoidal functors into the category of real vector spaces and linear maps equipped with the Schauenburg tensor product. We study representation theory of the (chromatic) Brauer category, and classify all its faithful linear representations. As an application, we use indices of fold lines to construct a refinement of Banagl’s concrete positive TFT based on fold maps into the plane.

scholarly journals Closed linear maps from a barrelled normed space into itself need not be continuous

1998 ◽  
Vol 57 (2) ◽  
pp. 177-179 ◽  
Author(s):  
José Bonet
Keyword(s):  
Normed Space ◽  
Continuous Linear ◽  
Closed Graph ◽  
Linear Map ◽  
Linear Maps ◽  
Barrelled Spaces

Examples of normed barrelled spacesEor quasicomplete barrelled spacesEare given such that there is a non-continuous linear map from the spaceEinto itself with closed graph.

Topological decompositions of the duals of locally convex operator spaces

1983 ◽  
Vol 93 (2) ◽  
pp. 307-314 ◽  
Author(s):  
D. J. Fleming ◽  
D. M. Giarrusso
Keyword(s):  
Uniform Convergence ◽  
Banach Spaces ◽  
Linear Subspace ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Operator Spaces ◽  
Natural Topology ◽  
Usual Norm ◽  
Linear Maps ◽  
Locally Convex

If Z and E are Hausdorff locally convex spaces (LCS) then by Lb(Z, E) we mean the space of continuous linear maps from Z to E endowed with the topology of uniform convergence on the bounded subsets of Z. The dual Lb(Z, E)′ will always carry the topology of uniform convergence on the bounded subsets of Lb(Z, E). If K(Z, E) is a linear subspace of L(Z, E) then Kb(Z, E) will be used to denote K(Z, E) with the relative topology and Kb(Z, E)″ will mean the dual of Kb(Z, E)′ with the natural topology of uniform convergence on the equicontinuous subsets of Kb(Z, E)′. If Z and E are Banach spaces these provide, in each instance, the usual norm topologies.

Sign in / Sign up

Export Citation Format

Share Document