Strictly Singular and Regular Integral Operators

Flores, Julio

doi:10.1007/s00020-005-1399-8

Integr. equ. oper. theory

2005

DOI: 10.1007/s00020-005-1399-8

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Strictly Singular and Regular Integral Operators

Julio Flores¹

Abstract: In the setting of Köthe function spaces we present some sufficient conditions for a regular integral operator to be strictly singular.

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2022

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Strictly singular non-compact operators between $L_p$ spaces

2022

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We study the structure of strictly singular non-compact operators between L_p spaces. Answering a question raised in earlier work on interpolation properties of strictly singular operators, it is shown that there exist operators T , for which the set of points (1/p,1/q)\in(0,1)\times (0,1) such that T\colon L_p\rightarrow L_q is strictly singular but not compact contains a line segment in the triangle \{(1/p,1/q):1<p<q<\infty\} of any positive slope. This will be achieved by means of Riesz potential operators between metric measure spaces with different Hausdorff dimension. The relation between compactness and strict singularity of regular (i.e., difference of positive) operators defined on subspaces of L_p is also explored.

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Strictly singular non-compact operators between $L_p$ spaces

2022

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Strictly Singular and Regular Integral Operators

Abstract: In the setting of Köthe function spaces we present some sufficient conditions for a regular integral operator to be strictly singular.

Cited by 1 publication

References 19 publications

Strictly singular non-compact operators between $L_p$ spaces

Strictly singular non-compact operators between $L_p$ spaces

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