Inequalities for the spectral radius and essential spectral radius of positive operators on Banach sequence spaces

Positivity ◽  
2021 ◽  
Author(s):  
Aljoša Peperko
Keyword(s):  
Spectral Radius ◽  
Positive Operators ◽  
Sequence Spaces ◽  
Essential Spectral Radius ◽  
Banach Sequence Spaces ◽  
Banach Sequence

Weak orthogonality and weak property (β) in some banach sequence spaces

1999 ◽  
Vol 49 (2) ◽  
pp. 303-316 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Ryszard Płuciennik
Keyword(s):  
Sequence Spaces ◽  
Banach Sequence Spaces ◽  
Weak Property ◽  
Banach Sequence

scholarly journals On the Dvoretzky-Rogers theorem

1984 ◽  
Vol 27 (2) ◽  
pp. 105-113
Author(s):  
Fuensanta Andreu
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Finite Dimensional ◽  
Banach Sequence Spaces ◽  
Perfect Sequence ◽  
Normal Topology ◽  
Banach Sequence

The classical Dvoretzky-Rogers theorem states that if E is a normed space for which l1(E)=l1{E} (or equivalently , then E is finite dimensional (see [12] p. 67). This property still holds for any lp (l<p<∞) in place of l1 (see [7]p. 104 and [2] Corollary 5.5). Recently it has been shown that this result remains true when one replaces l1 by any non nuclear perfect sequence space having the normal topology (see [14]). In this context, De Grande-De Kimpe [4] gives an extension of the Devoretzky-Rogers theorem for perfect Banach sequence spaces.

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