Banach-Steinhaus properties of strictly $$ \mathcal{N} $$-locally convex spaces based on the principle of uniform boundedness

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
S. Lahrech
Keyword(s):  
Uniform Boundedness ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Type Result ◽  
Locally Convex ◽  
Continuous Linear Operators ◽  
Convex Spaces

AbstractUsing the principle of uniform boundedness in a strictly $$ \mathcal{N} $$-locally convex spaces, we establish a Banach-Steinhaus-type result for sequentially continuous linear operators.

Linear Chaos on Fréchet Spaces

2003 ◽  
Vol 13 (07) ◽  
pp. 1649-1655 ◽  
Author(s):  
J. Bonet ◽  
F. Martínez-Giménez ◽  
A. Peris
Keyword(s):  
Linear Operators ◽  
Locally Convex Spaces ◽  
Fréchet Spaces ◽  
Continuous Linear ◽  
Locally Convex ◽  
Continuous Linear Operators ◽  
Convex Spaces

This is a survey on recent results about hypercyclicity and chaos of continuous linear operators between complete metrizable locally convex spaces. The emphasis is put on certain contributions from the authors, and related theorems.

Some special operators and new classes of locally convex spaces

1972 ◽  
Vol 71 (3) ◽  
pp. 475-489 ◽  
Author(s):  
Ajit Kaur Chilana
Keyword(s):  
Hausdorff Space ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Locally Convex ◽  
Continuous Linear Operators ◽  
Convex Spaces ◽  
Special Classes

AbstractWe consider some special operators on a locally convex Hausdorff space to itself, which have neat spectral theories and prove some perturbation results. This leads us to define and study a few special classes of locally convex spaces in which various subsets of the algebra of continuous linear operators either coincide or are closely related with each other. These are then compared to the classes of barrelled, infrabarrelled and DF-spaces and examples are given to distinguish them from one another.

Projections and embeddings of locally convex operator spaces and their duals

1984 ◽  
Vol 96 (2) ◽  
pp. 321-323 ◽  
Author(s):  
Jan H. Fourie ◽  
William H. Ruckle
Keyword(s):  
Dual Space ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Operator Spaces ◽  
Complemented Subspace ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Continuous Linear Operators

AbstractLet E, F be Hausdorff locally convex spaces. In this note we consider conditions on E and F such that the dual space of the space Kb (E, F) (of quasi-compact operators) is a complemented subspace of the dual space of Lb (E, F) (of continuous linear operators). We obtain necessary and sufficient conditions for Lb(E, F) to be semi-reflexive.

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 On numerical ranges of operators on locally convex spaces

1975 ◽  
Vol 20 (4) ◽  
pp. 468-482 ◽  
Author(s):  
J. R. Giles ◽  
G. Joseph ◽  
D. O. Koehler ◽  
B. Sims
Keyword(s):  
Numerical Range ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Range Theory ◽  
Locally Convex ◽  
Convex Spaces

Numerical range theory for linear operators on normed linear spaces and for elements of normed algebras is now firmly established and the main results of this study are conveniently presented by Bonsall and Duncan in (1971) and (1973). An extension of the spatial numerical range for a class of operators on locally convex spaces was outlined by Moore in (1969) and (1969a), and an extension of the algebra numerical range for elements of locally m-convex algebras was presented by Giles and Koehler (1973). It is our aim in this paper to contribute further to Moore's work by extending the concept of spatial numerical range to a wider class of operators on locally convex spaces.

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