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.

scholarly journals The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Convex Set ◽  
Locally Convex Spaces ◽  
Linear Spaces ◽  
Algebraic Interior ◽  
Vector Closure ◽  
Ordered Linear Spaces ◽  
The Relationship ◽  
Locally Convex ◽  
Convex Spaces

A new notion of the ic-cone convexlike set-valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces. The relationship between the ic-cone convexlike set-valued map and the nearly cone subconvexlike set-valued map is established. The results in this paper generalize some known results in the literature from locally convex spaces to linear spaces.

On Isomorphisms of Locally Convex Spaces With Similar Biorthogonal Systems

1973 ◽  
Vol 16 (2) ◽  
pp. 179-183
Author(s):  
F. Bozel ◽  
T. Husain
Keyword(s):  
Locally Convex Spaces ◽  
Linear Spaces ◽  
Biorthogonal Systems ◽  
Prove Theorem ◽  
Barrelled Spaces ◽  
The Relationship ◽  
Locally Convex ◽  
Convex Spaces

The relationship between bases and isomorphisms (i.e. linear homeomorphisms) between complete metrizable linear spaces has been studied with great interest by Arsove and Edwards (see [1] and [2]). We prove (Theorem 1) that in the case of B-complete barrelled spaces, similar generalized bases imply existence of an isomorphism. This result was also proved by Dyer and Johnson [4], so we do not give a proof. We show (Theorem 6) that if one assumes that the bases are Schauder and similar, then Theorem 1 holds for countably barrelled spaces. We use Theorem 1 to advantage (Theorems 2-5) to show that one can improve some results due to Davis [3].

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.

Sign in / Sign up

Export Citation Format

Share Document