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The Trace of Nuclear Operators on L p(μ) for σ-Finite Borel Measures on Second Countable Spaces

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Abstract

Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets \({\mathcal{M}}\). Let T be a nuclear operator on \({L^p({\Omega},{\mathcal{M}},\mu) }\), 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on operator ideals introduced by Pietsch and a characterization of nuclear operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal.

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Authors and Affiliations

  1. Universidad del Valle, Calle 13, 100-00, Cali, Colombia

    Julio Delgado

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  1. Julio Delgado
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Correspondence to Julio Delgado.

Additional information

This work has been partially supported by Universidad del Valle, Vicerrectoria Inv. Grant#7756.

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Delgado, J. The Trace of Nuclear Operators on L p(μ) for σ-Finite Borel Measures on Second Countable Spaces. Integr. Equ. Oper. Theory 68, 61–74 (2010). https://doi.org/10.1007/s00020-010-1813-8

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  • DOI: https://doi.org/10.1007/s00020-010-1813-8

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