A spectral mapping theorem for scalar-type spectral operators in locally convex spaces

1985 ◽  
Vol 8 (2) ◽  
pp. 276-288 ◽  
Author(s):  
W. Ricker
Keyword(s):  
Locally Convex Spaces ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Scalar Type ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Degenerate abstract Volterra equations in locally convex spaces

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 597-619
Author(s):  
Marko Kostic
Keyword(s):  
Resolvent Operator ◽  
Final Section ◽  
Differential Operators ◽  
Volterra Equations ◽  
Locally Convex Spaces ◽  
Efficient Tool ◽  
Scalar Type ◽  
Locally Convex ◽  
Resolvent Families ◽  
Convex Spaces

In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

ON THE PRINCIPLE OF UNIFORM BOUNDEDNESS FOR LSC CONVEX PROCESSES IN A STRICTLY N LOCALLY CONVEX SPACES

2008 ◽  
Vol 41 (1) ◽  
Author(s):  
S. Lahrech ◽  
A. Jaddar ◽  
J. Hlal ◽  
A. Ouahab ◽  
A. Mbarki
Keyword(s):  
Uniform Boundedness ◽  
Locally Convex Spaces ◽  
Convex Processes ◽  
Locally Convex ◽  
Convex Spaces

DENTABILITY IN LOCALLY CONVEX SPACES

1991 ◽  
Vol 14 (1) ◽  
pp. 105-110
Author(s):  
Neill Robertson
Keyword(s):  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals A characterization of Pontryagin–van Kampen duality for locally convex spaces

2002 ◽  
Vol 121 (1-2) ◽  
pp. 75-89 ◽  
Author(s):  
Fernando Garibay Bonales ◽  
F.Javier Trigos-Arrieta ◽  
Rigoberto Vera Mendoza
Keyword(s):  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces
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