Inequalities for the Hadamard Weighted Geometric Mean of Positive Kernel Operators on Banach Function Spaces

Positivity ◽  
2006 ◽  
Vol 10 (4) ◽  
pp. 613-626 ◽  
Author(s):  
Roman Drnovšek ◽  
Aljoša Peperko
Keyword(s):  
Geometric Mean ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Positive Kernel ◽  
Kernel Operators

Spectral inequalities for compact integral operators on Banach function spaces

1992 ◽  
Vol 112 (3) ◽  
pp. 589-598 ◽  
Author(s):  
Roman Drnovšek
Keyword(s):  
Integral Operator ◽  
Spectral Radius ◽  
Geometric Mean ◽  
Integral Operators ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Compact Integral Operator

AbstractThis article generalizes some spectral inequalities for non-negative matrices (see [2] and [3]) to compact integral operators with non-negative kernels defined on Banach function spaces. The spectral radius of a sum of such operators is estimated under certain conditions and a generalization of this inequality is given. An inequality for the spectral radius of a compact integral operator with the kernel equal to a weighted geometric mean of non-negative kernels is also proved.

FACTORIZING MULTILINEAR KERNEL OPERATORS THROUGH SPACES OF VECTOR MEASURES

2020 ◽  
pp. 1-22
Author(s):  
ORLANDO GALDAMES-BRAVO
Keyword(s):  
Homogeneous Polynomial ◽  
Function Spaces ◽  
Linear Operators ◽  
Order Continuity ◽  
Banach Function Spaces ◽  
Vector Measures ◽  
Kernel Operator ◽  
Continuity Properties ◽  
Finite Measures ◽  
Kernel Operators

We consider a multilinear kernel operator between Banach function spaces over finite measures and suitable order continuity properties, namely $T:X_{1}(\,\unicode[STIX]{x1D707}_{1})\times \cdots \times X_{n}(\,\unicode[STIX]{x1D707}_{n})\rightarrow Y(\,\unicode[STIX]{x1D707}_{0})$ . Then we define, via duality, a class of linear operators associated to the $j$ -transpose operators. We show that, under certain conditions of $p$ th power factorability of such operators, there exist vector measures $m_{j}$ for $j=0,1,\ldots ,n$ so that $T$ factors through a multilinear operator $\widetilde{T}:L^{p_{1}}(m_{1})\times \cdots \times L^{p_{n}}(m_{n})\rightarrow L^{p_{0}^{\prime }}(m_{0})^{\ast }$ , provided that $1/p_{0}=1/p_{1}+\cdots +1/p_{n}$ . We apply this scheme to the study of the class of multilinear Calderón–Zygmund operators and provide some concrete examples for the homogeneous polynomial and multilinear Volterra and Laplace operators.

scholarly journals Non-commutative Banach function spaces

1989 ◽  
Vol 201 (4) ◽  
pp. 583-597 ◽  
Author(s):  
Peter G. Dodds ◽  
Theresa K. -Y. Dodds ◽  
Ben de Pagter
Keyword(s):  
Function Spaces ◽  
Banach Function Spaces

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
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