Multi-Dimensional spectral theory of bounded linear operators in locally convex spaces

1986 ◽  
Vol 275 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Volker Wrobel
Keyword(s):  
Spectral Theory ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space

1988 ◽  
Vol 31 (1) ◽  
pp. 127-144 ◽  
Author(s):  
B. P. Rynne
Keyword(s):  
Hilbert Space ◽  
Spectral Theory ◽  
Linear Operators ◽  
Coupled Systems ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Joint Spectrum ◽  
Image Position

Let n≧1 be an integer and suppose that for each i= 1,…,n, we have a Hilbert space Hi and a set of bounded linear operators Ti, Vij:Hi→Hi, j=1,…,n. We define the system of operatorswhere λ=(λ1,…,λn)∈ℂn. Coupled systems of the form (1.1) are called multiparameter systems and the spectral theory of such systems has been studied in many recent papers. Most of the literature on multiparameter theory deals with the case where the operators Ti and Vij are self-adjoint (see [14]). The non self-adjoint case, which has received relatively little attention, is discussed in [12] and [13].

scholarly journals Five short lemmas in Banach spaces

2016 ◽  
Vol 32 (1) ◽  
pp. 131-140
Author(s):  
QINGPING ZENG ◽  
Keyword(s):  
Banach Spaces ◽  
Spectral Theory ◽  
Commutative Diagram ◽  
Spectral Properties ◽  
Linear Operators ◽  
General Question ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Local Spectral Theory

Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.

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.

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.

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