Kernel Operators

2017 ◽  
pp. 51-91
Keyword(s):  
Kernel Operators

Function spaces arising from kernel operators

Positivity ◽  
2010 ◽  
Vol 14 (4) ◽  
pp. 637-653
Author(s):  
Guillermo P. Curbera ◽  
Werner J. Ricker
Keyword(s):  
Function Spaces ◽  
Kernel Operators

scholarly journals Banach lattices with the fatou property and optimal domains of kernel operators

2006 ◽  
Vol 17 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Guillermo P. Curbera ◽  
Werner J. Ricker
Keyword(s):  
Banach Lattices ◽  
Fatou Property ◽  
Kernel Operators

scholarly journals Ideal structure and factorization properties of the regular kernel operators

Positivity ◽  
2019 ◽  
Vol 24 (5) ◽  
pp. 1211-1229
Author(s):  
A. Blanco
Keyword(s):  
Banach Lattice ◽  
Weak Order ◽  
Ideal Structure ◽  
Order Unit ◽  
Factorization Property ◽  
Kernel Operator ◽  
Regular Kernel ◽  
And Algebra ◽  
Kernel Operators ◽  
The Ideal

AbstractWe consider the structure of the lattice of (order and algebra) ideals of the band of regular kernel operators on $$L^p$$ L p -spaces. We show, in particular, that for any $$L^p(\mu )$$ L p ( μ ) space, with $$\mu $$ μ $$\sigma $$ σ -finite and $$1<p<\infty $$ 1 < p < ∞ , the norm-closure of the ideal of finite-rank operators on $$L^p(\mu )$$ L p ( μ ) , is the only non-trivial proper closed (order and algebra) ideal of this band. Key to our results in the $$L^p$$ L p setting is the fact that every regular kernel operator on an $$L^p(\mu )$$ L p ( μ ) space ($$\mu $$ μ and p as before) factors with regular factors through $$\ell _p$$ ℓ p . We show that a similar but weaker factorization property, where $$\ell _p$$ ℓ p is replaced by some reflexive purely atomic Banach lattice, characterizes the regular kernel operators from a reflexive Banach lattice with weak order unit to a KB-space with weak order unit.

scholarly journals On the lattice structure of kernel operators

2014 ◽  
Vol 288 (5-6) ◽  
pp. 584-592 ◽  
Author(s):  
Moritz Gerlach ◽  
Markus Kunze
Keyword(s):  
Lattice Structure ◽  
Kernel Operators

A CHARACTERIZATION OF THE BAND OF KERNEL OPERATORS

1980 ◽  
Vol 4 (2) ◽  
pp. 89-107 ◽  
Author(s):  
Jacobus J Grobler ◽  
Peter van Eldik
Keyword(s):  
Kernel Operators
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